 |
Consortional main: Research in Number Theory
|
Help 
Print 
|
Here you can view and search the projects funded by NKFI since 2004
Back »
|
| |
Details of project |
|
|
| Identifier |
104183 |
| Type |
NK |
| Principal investigator |
Pintz, János |
| Title in Hungarian |
Konzorcium, fő p.: Számelméleti kutatások |
| Title in English |
Consortional main: Research in Number Theory |
| Keywords in Hungarian |
számelmélet,analitikus számelmélet, kombinatorikus számelmélet, diofantikus számelmélet |
| Keywords in English |
number theory,analytic number theory, combinatorical number theory, diophantine number theory |
| Discipline |
| Mathematics (Council of Physical Sciences) | 100 % | | Ortelius classification: Number theory |
|
| Panel |
Mathematics and Computing Science |
| Department or equivalent |
Alfréd Rényi Institute of Mathematics |
| Participants |
Balog, Antal
Biró, András
Gyarmati, Katalin
Harcos, Gergely
Károlyi, Gyula
Katona, Gyula
Krenedits, Sándor
Lapkova, Kostadinka
Maga, Péter
Révész, Szilárd
Ruzsa, Imre
Sárközy, András
Solymosi, Jozsef
Szemerédi, Endre
Tóth, Árpád
|
| Starting date |
2013-02-01 |
| Closing date |
2017-12-31 |
| Funding (in million HUF) |
32.977 |
| FTE (full time equivalent) |
20.20 |
| state |
closed project |
Summary in Hungarian A kutatás összefoglalója, célkitűzései szakemberek számára
Itt írja le a kutatás fő célkitűzéseit a témában jártas szakember számára.
Tervezett kutatásaink a Budapesti Erdős-Turán iskola és a Debreceni Számelméleti Iskola több évtizedes hagyományaira és eredményeire épülnek. Ennek megfelelően a meghatározó kutatási irányok az analitikus, kombinatorikus számelmélet és diofantikus egyenletek területére esnek vagy azokkal szoros kapcsolatban vannak. Ennek megfelelően kutatásokat tervezünk folytatni a prímek eloszlására és additív tulajdonságaira, tigonometrikus összegek, automorf és moduláris formákra, kombinatorikus számelméletre és additív kombinatorikára vonatkozólag, továbbá végesen generált integritási tartományok feletti diofantikus egyenletek effektív elméletében, polinomok felbonthatóságával és hatványösszegeket tartalmazó diofantikus egyenletek megoldásával kapcsolatban, algebrai görbékre és felületekre illeszkedő számtani sorozatokról valamint számtani sorozatokban előforduló hatványokról.
Bár a tervezett konkrét kutatások a matematika elég jól körülhatárolható területére esnek, mégsem lehet egyetlen kutatási célt megfogalmazni, mert az a konkrét probléma természetétől és általánosságától függ.
Kutatásaink másik fontos iránya a számelmélet kriptográfiai alkalmazása. Itt álvéletlenszám generátorokkal, matematikai eszközökkel definiált hash függvényekkel valamint az anonimitás alkalmazásaival és megvalósíthatóságával kapcsolatban tervezünk kutatásokat folytatni.
A kriptográfia területén a számelméletből ismert eredményeket és módszereket alkalmazzuk kriptográfiai primitívek és protokollok kidolgozására. Fontosnak tekintjük, hogy a konstrukcióinkról matematikai bizonyítható tételeket találjunk.
Mi a kutatás alapkérdése?
Ebben a részben írja le röviden, hogy mi a kutatás segítségével megválaszolni kívánt probléma, mi a kutatás kiinduló hipotézise, milyen kérdéseket válaszolnak meg a kísérletek.
A kutatásunknak több alapkérdése is van, A Debreceni Egyetem társpályázatának fő kérdése a következőképp foglalható össze: David Hilbert 1900-ban megfogalmazott problémája olyan eljárás megalkotására vonatkozott, amellyel minden diofantikus egyenletekről el lehet dönteni, hogy megoldható-e. Yurij Matijaszevics 1970-ben megmutatta, hogy ilyen általános algoritmus nem létezik. Hilbert programja tehát csak diofantikus egyenletek meghatározott osztályaira oldható meg. Ilyeneket a XX. sz. folyamán, nem kis részben a Debreceni Számelméleti Iskola közreműködésével, sikerült is definiálni és a tételek hatókörét lényegesen ki lehetett bővíteni. Kutatásaink alapkérdése tehát olyan tételek bizonyítása, amelyek diofantikus egyenletek minél szélesebb körében biztosítja a megoldhatóság algoritmikus eldöntését és lehetővé teszi konkrét egyenletek minél általánosabb osztályaira a megoldások meghatározását.
A főpályázat kérdéseit nehezebben lehet összefoglalni: 2 fő szempontot emelnénk ki.
1) Szemerédi híres tétele, az általa bizonyított Regularitási lemma és pszeudorandom módszere az additív kombinatorikai módszerek legfontosabbjaivá vált; döntő szerepük volt Green-Tao Fields Medalt nyert világhíres tételének bizonyításában. Egyik fő problémánk a tetszőleges struktúrákban meghúzódó szabályosságok vizsgálata.
2) A prímszámok azok az elemi részecskék, amelyekből az egészek multiplikatív félcsoportja felépül, míg az additív csoportjuk egy végtelen ciklikus csoport A két struktúra összekapcsolása bármilyen módon a lehető legnehezebb kérésekre vezet: elegendő a Goldbach és ikerprím problémákkal, prímek számtani sorozatok-beli eloszlásával kapcsolatos kérdések említése.
Mi a kutatás jelentősége?
Röviden írja le, milyen új perspektívát nyitnak az alapkutatásban az elért eredmények, milyen társadalmi hasznosíthatóságnak teremtik meg a tudományos alapját. Mutassa be, hogy a megpályázott kutatási területen lévő hazai és a nemzetközi versenytársaihoz képest melyek az egyediségei és erősségei a pályázatának!
A matematikai kutatások egyik legalapvetőbb célja egyenletek megoldása. Ha a megoldások halmazát az egész számokra szűkítjük, akkor kapjuk a diofantikus egyenleteket, amelyek évezredek óta foglalkoztatják a matematikusokat. Kutatási eredményeink ezen a területen évtizedek óta a nemzetközi szakmai élvonalba tartoznak. A projekt során legalább meg akarjuk tartani ezt a pozíciónkat. Általánosítani akarunk ismert tételeket, illetve új kutatási irányokat kezdeményezünk, azaz alkalmazásokat keresünk ismert tételekre vagy olyan módszereket dolgozunk ki, amelyek lehetővé teszik korábban megtámadhatatlan egyenletek megoldását.
A kutatás információt nyújthat az egész számok tetszőleges, csak bizonyos sűrűségi feltételeknek eleget tevő részhalmazainak tulajdonságaiba, továbbá olyan rendkívül fontos determinisztikus sorozatok eloszlásí tulajdonságaiba, mint a prímszámok. Általánosabban is kapcsolatot teremthetünk az egész számok multiplikatív és additív tulajdonságai között, mint az úgynevezett összeg-szorzat halmazok.
Kapcsolatokat tudunk feltárni a prímszámok eloszlásában megmutatkozó szabályosságok és szabálytalanságok között, és olyan világhíres, több évszázados, vagy esetleg több évezredes problémák megközelítésére vonatkozóan bizonyíthatunk tételeket, mint a Goldbach sejtés és az ikerprím sejtés.
Tervezett kriptográfiai kutatásaink alapkutatások. Olyan kriptográfiai primitíveket dolgozunk ki, amelyek tulajdonságait minél általánosabb feltételek mellett be lehet bizonyítani. Ilyen eredményeknek az a jelentősége, hogy megismerjük a módszerek alkalmazhatóságának a határait. Bízunk benne, hogy eredményeink, bizonyos feltételek mellett a gyakorlatban is alkalmazhatóak.
A kutatás összefoglalója, célkitűzései laikusok számára
Ebben a fejezetben írja le a kutatás fő célkitűzéseit alapműveltséggel rendelkező laikusok számára. Ez az összefoglaló a döntéshozók, a média, illetve az érdeklődők tájékoztatása szempontjából különösen fontos az NKFI Hivatal számára.
Kutatásaink nagyobb és fontosabb része a diofantikus egyenletek megoldásával foglalkozik. Ezek olyan egyenletek, amelyeknek a megoldásait az egész számok körében keressük és évezredek óta a matematikai kutatások fontos területét jelentették. A stratégiai cél a megoldások meghatározása. Ez azonban csak bizonyos, szűk körben érhető el. Kutatásaink során ezt a kört szeretnénk minél jobban bővíteni. A kézzel vagy számítógéppel megoldható egyenletek azok közé tartoznak, amelyek megoldására algoritmust tudunk adni. Az algoritmussal elvileg megoldható egyenletek körének bővítése is fontos célunk.
Kutatásaink másik fókusza a prímszámok eloszlásának tulajdonságai, melyek meghatározásuk szerint pontosan két osztóval rendelkeznek, eggyel és önmagunkkal. Több ezer éve tudjuk (bár precíz igazolása csak 1800-ban Gaussnak sikerült), hogy a pozitív egészek pontosan egyféleképp írhatóak fel (sorrendtől eltekintve) prímszámok szorzataként. Ugyanakkor a prímszámok eloszlása tekintetében nagyon sok egyszerűen megfogalmazható és világhíres matematikusok által több száz éve vizsgált kérdésre nem tudjuk a választ, mint pl. az ikerprímsejtés, azaz, hogy van-e végtelen sok egymástól csak 2-vel különböző ún. ikerprímszám (a legjobb eredményt a témavezető érte el 2 külföldi kutatóval együtt). Ezen problémákban szeretnénk előbbre jutni.
Kutatásaink másik területe az algoritmikus adatvédelem, a kriptográfia elméleti alapjaival foglalkozik. Számelméleti ismereteinkre, eredményeinkre és tapasztalatainkra alapozva kriptográfiai algoritmusok és protokollok kidolgozásával, és matematikai elemzéssel foglalkozunk. Célunk például az elektronikus választás, ill. vizsgáztatás protokolljainak vizsgálata.
| Summary Summary of the research and its aims for experts
Describe the major aims of the research for experts.
Our research proposal is based on the many decades long traditions and on the results of the Erdős-Turán school in Budapest and on the Debrecen Number Theory School. According to this the main research aresas to be studied are the following: analytic number theory, combinatorial number theory, additive combinatorics and the theory of diophantine equations, further topics closely related to them. We plan to do research concerning the distribution of primes additive prime number theory, trigonometric sums, automorphic and modular forms, combinatorial number theory and additive combinatorics. We plan to investigate effective theory of diophantine equations over finitely generated integral domains, decomposition of polynomials and certain diophantine equations concerning power sums, arithmetical progressions on algebraic curves and power values of arithmetical progressions.
Although the concrete research we plan is connected to a well defined area of mathematics, still we cannot specify only one research goal, since it depends on the nature and generality of the problem.
Another essential direction of our research is cryptographic application of number theoretical results. We would like to study pseudorandom number generation, hash functions defined by mathematical tools, applications of anonymity.
In the theory of cryptography we employ number theoretical methods and results to develop cryptographic primitives and protocols. We find it important to give theorems about our construction with detailed mathematical proofs.
What is the major research question?
Describe here briefly the problem to be solved by the research, the starting hypothesis, and the questions addressed by the experiments.
Our research plan has several main objectives. The main objective of our research partner, the Debrecen University can be described as follows: In 1900, David Hilbert formulated as the main problem of the diophantine number theory to give a procedure that is able to output whether a diophantine equation is solvable or not.
In 1970, Yurij Matijaszevics showed that there is no general algorithm for it. Hilbert's problem can be solved only for some specified classes of diophantine equations. During the 20th century, partly through the contribution of the Number Theory School of Debrecen most of these classes are defined and theorems are extended. The fundamental question of our research is to prove theorems that provide results about solvability of diophantine equations and give algorithms to find solutions of large families of diophantine equations.
It is more difficult to summarize the research proposal concerning analytic and combinatorial number theory: we mention 2 main points.
1)The famous theorem of Szemerédi, his regularity lemma and the pseudorandom method initiated by him became the most important tools of additive combinatorics; they played a decisive role in the celebrated theorem of Green and Tao, for which Tao earned the Fields Medal. We would like to investigate regularity properties of general structures.
2)Prime numbers are like elementary particles: they generate the multiplicative semigroup of the integers, while their additive group is a simple infinite cyclic group. The connection between these 2 structures leads to increduibly difficult problems, like the Goldbach or twin-prime problems or the distribution of primes in arithmetic progressions.
What is the significance of the research?
Describe the new perspectives opened by the results achieved, including the scientific basics of potential societal applications. Please describe the unique strengths of your proposal in comparison to your domestic and international competitors in the given field.
Importance of mathematical research is to solve equations. If we narrow the set of solutions to integers, then we get diophantine equations that have been very interesting for mathematicians for a long time. Our results are internationally well-known and considered outstanding for decades. During the project we would like to maintain our reputation. We would like to generalize well-known theorems, and introduce new research directions: we search applications of well-known theorems and develop methods that help to solve equations that seemed to be extremely difficult to solve before.
The other focus of our researh proposal is to obtain information about subsets of the positive integers, characterised merely by some density properties, further to obtain information about the distribution of such important deterministic sequences like the primes. More generally we can establish connections between the multiplicative and additive structures of integers like the sum-product theorems. We can reveal connections between regularities and irregularities of the distribution of primes and can prove theorems about the approximation of such world famous (centuries old) problems like the Goldbach and twin prime problems.
Our research in cryptography is basic. We develop cryptographic primitives with properties that can be proved under general conditions. Importance of these results is to study the limit of our methods. Hopefully, our solutions, under certain conditions can be applied in practice, too.
Summary and aims of the research for the public
Describe here the major aims of the research for an audience with average background information. This summary is especially important for NRDI Office in order to inform decision-makers, media, and others.
Important part of our research is related to solutions of diophantine equations. Diophantine equations are equations with solutions in the set of integers, mathematicians are interested in them for long time. The goal is to determine the solutions, but it is possible only for special classes of equations. Our goal is to extend the set of these classes as much as possible. If we can solve an equation either by hand or by computer, then we can give an algorithm to find solutions. It is important for us to extend the set of solvable equations.
Another main part of our research proposal is the distribution of primes (that is, numbers with exactly two divisors: 1 and the number itself. Positive integers can be written in a unique way (up to the permutation of the factors) as a product of primes (EUclid, 2300 B.C., exactly: Gauss, 1800). On the other hand we have many problems about primes, which can be formulated and understood easily; nevertheless, despite of all the efforts of the best mathematicians of the world we still do not know the answers for them. Such an example is provided, e.g. by the twin prime conjecture which states that there are infinitely many pairs of primes with differense 2 (the best result was reached by Goldston, Pintz and Yildirim). We would lik e to reach progress in these problems too.
The other area of our research is related to theoretical foundations of algorithmic data security, i. e. cryptography. Based on our number theoretical knowledge, results we deal with cryptographical algorithms and protocols and their mathematical analysis. Our aim is for example to investigate electronic elections and exam systems.
|
|
|
|
|
|
|
|
| |
List of publications |
|
|
| Bazsó A., Mező I.: Some notes on alternating power sums of arithmetic progressions, Journal of Integer Sequences, to appear, 2018 | | Bazsó A., Bérczes A., Hajdu L., Luca F.: Polynomial values of sums of products of consecutive integers, Mh. Math. , to appear, 2018 | | Bugeaud Y, Evertse J. H., Győry K.: S-parts of values of univariate polynomials, binary forms and decomposable forms at integral points, Acta Arith., to appear, 2018 | | Bertók Cs., Hajdu L., Pethő A. Schinzel A.: On the smallest number of terms of vanishing sums of units in number fields, J. Number Theory, to appear, 2018 | | Bérczes A.: Effective results for Diophantine problems over finitely generated domains, MTA doktori disszertáció, 2017 | | Bérczes A., Pink I, Savas G., Soydan G.: On the diophantine equation (x+1)^k + (x+2)^k + ... +(2x)^k = y^n, J. Number Theory 183, 326-351., 2018 | | Folláth J., Herendi T.: Two Stage Gaussian Sampling II: Complexity estimates, to appear, 2018 | | Győry K., Hajdu L., Tijdeman R.: Representation of finite graphs as difference graphs of S-units II, Acta Math. Hungar. 149, 423-447., 2016 | | Huszti A., Oláh N.: A Simple Authentication Scheme for Clouds, IEEE Conference on Commmunication and network Security (SPC 2016), pp. 565-569., 2016 | | Pintér Á., Rakaczki Cs.: On the decomposability of linear combinations of Euler polynomials, Mathematical Notes - Miskolc 181, 407-415., 2017 | | Tengely Sz.: Composite Rationalk Functions and Arithmetic Progressions, Publ. Math. Debrecen, to appear, 2018 | | Tengely, Sz., Ulas M.: On a problem of Pethő, J. Symbolic Computations, to appear, 2018 | | Tengely Sz., Ulas M.: On products of disjoint blocks of arithmetic progressions and related questions, J. Number Theory 165, 67-83, 2016 | | Zsuga J, Erdei T, Szabó K, Kampe N., Papp P., Pintér Á., Szentmiklósi A.J., Juhász B., Szilvássy Z., Gesztelyi R.: Methodical Challenges and a Possible Resolution in the Assessment of Receptor Reserve for Adenosine, an Agonist with Short Half-Life, Molecules 22, Paper E839, 17 pp., 2017 | | Hladky J., Komlós J., Piquet D., Simonovits M., Stein M., Szemerédi E.: The approximate Loebl-Komlós-Sós conjecture and embedding trees in sparse graphs, Electron. Res. Announc. Math. Sci. 22, 1-15, 2015 | | Szemerédi E.: Arithmetic progressions, different regularity lemmas and removal lemmas, Commun. Math. Stat. 3, no.3, 315-328., 2015 | | Szemerédi E.: Erdős's unit distance problem, Open problems in Mathematics, Springer, (Cham), pp. 459-477., 2016 | | Szemerédi, E.: Structural approach to subset sum problems, Found. Comput. Math. 16, no.6, 1737-1749., 2016 | | Rödl, V., Rucinsky A., Schacht, M. Szemerédi E.: On the Hamiltonicity of triple systems with high minimum degree, Ann. Comb. 21, no.1, 95-117., 2017 | | Pintz J.: On the ratio of consecutive gaps between primes, Analytic Number Theory, Springer, Cham, pp. 285-304., 2015 | | Hladky J., Komlós J., Piquet D., Simonovits M., Stein M., Szemerédi E.: The approximate Loebl-Komlós-Sós conjecture I: The sparse decomposition, SIAM J. Discrete Math. 31, no2, 945-982., 2017 | | Hladky J., Komlós J., Piquet D., Simonovits M., Stein M., Szemerédi E.: The approximate Loebl- Komlós-Sós conjecture II: The rough structure of LKS graphs, SIAM J. Discrete Math. 31, no. 2, 983-1016., 2017 | | Hladky J., Komlós J., Piquet D., Simonovits M., Stein M., Szemerédi E.: The approximate Loebl-Komlós-Sós conjecture III: The finer structure of LKS graphs, SIAM J. Dicrete Math. 31, no.2, 1017-1071., 2017 | | Hladky J., Komlós J., Piquet D., Simonovits M., Stein M., Szemerédi E.: The approximate Loebl-Komlós-Sós conjecture IV: Embedding techniques and the proof of the main result, SIAM J. Discrete Math. 31, no. 2, 1072-1148., 2017 | | Faghani M., Katona G.O.H.,: Results on the Wiener profile, AKCE International Journal of Graphs and Combinatorics, to appear, 2018 | | Horváth M., Ruzsa I.Z.: Connections between the cardinality of sumsets and difference sets near the extreme, Ann. Univ. Sci. Budapest 59, 137-142., 2016 | | Guerreiro J., Ruzsa I.Z.: Monochromatic paths for the integers, European J. Comb 58, 283-288., 2016 | | Glazryna P. Révész Sz.: Turán type oscillation inequalities in L_q norm on the boundary of convex domains, Math. Inequal. Appl., 20, No.1, 149-180., 2017 | | Glazyrina P., Révész Sz.: Turán type converse Markov inequalities in L_q on a generalized Erod class of convex domains, J. Approx. Theory 221, 62-76., 2017 | | Krenedits S., Révész Sz.: The point value maximization problem nfor positive definite functions supported in a given subset of a locally compact group, Proc. Edinb. Math. Soc., to appear, 2018 | | Katona G.O.H.: A general 2-part Erdős-Ko-Rado theorem, Opuscula Mathematica 37, no.4, 577-588., 2017 | | Harcos G: Primek, Polignac, Polymath, Mat. Lapok (N.S.) 20, no.2, 1-13., 2014 | | Bérczes A., Dujella A., Hajdu A., Tengely Sz.: Finiteness results for F-Diophantine sets, Mh. Math., 180, 469-484., 2016 | | Evertse, J.H., Győry, K.: Discriminant Equations in Diophantine Number theory, Cambridge University Press, 2017 | | Tengely, Sz.: On a peoblem of Erdős and Graham, Periodica Math. Hung. 72, no.1, 23-28., 2016 | | D. Kaptan: A note on small gaps between primes in arithmetic progressions, Acta Arith. 172, no.4, 351-375., 2016 | | J. Pintz: An approximation to the twin prime conjecture and the parity phenomenon, Indag. Math. 26, 883-896., 2015 | | Bárány I., Solymosi J.: Gershgorin disks for multiple eigenvalues of non-negative matrices, A Journey Through Discrete Mathematics, A Tribute to Jiří Matoušek Eds. Loebl, M., Nešetřil, J., Thomas, R., Springer, pp. 123-133, 2017 | | Dartyge, C., Gyarmati, K., Sárközy A.: On irregularities of distribution of binary sequences relative to arithmetic progressions, I (General results), Unif. Distr. Theory, 12 (1), 55-67, 2017 | | Pintz J.: Patterns of primes in arithmetic progressions, Number Theory – Diophantine Problems, Uniform Distribution and Applications, Festschrift in Honour of Robert F. Tichy, Eds. Ch. Elsholtz, P. Grabner, Springer, pp.369-379, 2017 | | Bérczes A., Luca F., Pink I., Ziegler V.: On trinomials with integral S-unit coefficients having a quadratic factor, Indag. Math. 28, 1200-1209, 2017 | | Evertse, J. H., Győry, K.: Discriminant equations in diophantine number theory, Cambridge University Press, 2016 | | Evertse, J. H., Győry, K.: Effective results for discriminant equations over finitely generated domains, Number Theory - Diophantine problems, Uniform distribution and applications,Springer, pp. 237-256., 2017 | | Bertók Cs., Hajdu L., Pethő A.: On the distribution of polynomials with bounded height, J. Number Theory 179, 172-184., 2017 | | Akiyama, S., Evertse, J.-H., Pethő, A.: On nearly linear recurrence sequences, Number Theory - Diophantine problems, Uniform Distribution and Applications - Festschrift in Honour of Robert F. Tichy's 60th Birthday, Eds.: Elsholtz, Grabner, pp.1-24, 2017 | | Fulek R., Mojarrad H.N., Naszódi M., Solymosi J., Stich S.U., Szedlák M.: On the existence of ordinary triangles, Computational Geometry 66, pp. 28-31, 2017 | | Solymosi J., Wong Ching,: On the number of non-intersecting hexagons in 3-space, Discrete Geometry and Convexity, BÁRÁNY 70, Springer, pp. 102-106, 2017 | | Dvir Z., Garg A., Oliveira R., Solymosi J.,: Rank bounds for design matrices with block entries and geometric applications, Discrete Analysis, to appear, 2018 | | Solymosi J., Wong Ching: An application of kissing number in sum-product estimates, Acta Math. Hungar., to appear, 2018 | | Gyarmati K,: On the cross-combined measure of families of binary lattices and sequences, Lecture Notes in Computer Science, 2018 | | Dartyge C., Gyarmati K., Sárközy Á.: On irregularities of distribution of binary sequences relative to erithmetic progressions, II (Special sequences), Unif. Distr. Theory, to appear, 2018 | | Gyarmati K., Sárközy A.: On reducible and primitive subsets of F_p, II., Quart. J. Math. Oxford 68 (1), 59-77., 2017 | | Mauduit C., Rivat J., Sárközy A.: On the digits of sumsets, Canadian J. Math. 69 (3), 595-612., 2017 | | Mauduit C., Rivat J., Sárközy A.: On the distribution of digits of sumns a+b, Ramanujan J., to appear, 2018 | | Mérai L., Rivat J., Sárközy A.: The measures of pseudorandomness and the NIST Tests,, Lecture Notes in Computer Science, to appear, 2018 | | Bíró A.: Local averages of the hyperbolic circle problem for Fuchsian groups, Mathematika, to appear, 2018 | | Bíró A.: Some integrals of hypergeometric functions, Acta Math. Hungar. 152, no. 1, 58-71., 2017 | | Efimov, A., Gaál M., Révész S.G.,: On integral estimates of nonnegative positive definite functions, Bull. Austr. Math. Soc. 96, no.1, 117-125., 2017 | | Gyula O.H. Katona, Daniel T. Nagy,: Incomparable copies of a poset in the Boolean lattice, Order, 32(2015) 419-427., 2015 | | Gyula O.H. Katona: Turán's graph theorem, measure and probability, in: Number theory, Analysis, and Combinatorics, Proceedings of the Paul Turán Memorial conference held Augiust 22-26, 2011 in Budapest, de Gruyter,, 2014 | | G.O.H. Katona,D. T. Nagy: Union-intersecting set systems, Graphs and Combinatorics 31, 1507-1516., 2015 | | Sárközy A.: On pseudorandomness of families of binary sequences, J. Applied Discrete Math. 216 (3), 670-676, 2017 | | He Bo; Pintér Á; Togbé A; Varga N: A generalization of a problem of Mordell, Glasnik Matematicki, 50(70) 35-41., 2015 | | J. Pintz: Polignac numbers, Conjecture of Erdős on Gaps between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture,, in: From Arithmetic to Zeta-Functions - Number Theory on Memory of Wolfgang Schwarz, Eds. J. Sander, J. Steuding, R. Steuding, Springer, 367-384, 2016 | | Gyula O.H. Katona: Turán's graph theorem, measure and probability, in: Number theory, Analysis, and Combinatorics, Proceedings of the Paul Turán Memorial conference held Augiust 22-26, 2011 in Budapest, de Gruyter, 2014 | | Ruzsa I. Z.: More differences than multiple sums, Combinatorica, to appear, 2017 | | Biró A., Lapkova, K.: The class number one problem for the real quadratic fields $\mathbb{Q}\left(\sqrt{(an)^2+4a}\right)$, Acta Arithmetica 172 (2), 117-131, 2016 | | Duke, W. D., Imamoglu, Ö., Tóth Á.: Geometric invariants for real quadratic fields, Annals of Math. 184 (3), 949-990, 2016 | | Duke W. D., Imamoḡlu Ö., Tóth Á.: Modular cocycles and linking numbers, Duke Math. J., to appear, 2017 | | Lapkova, K., Biro, A.: The class number one problem for the real quadratic fields Q(\sqrt{(an)^2+4a}), Acta Arith. 172 no. 2, 117-131, 2016 | | Lapkova, K.: On the k-free values of the polynomial xy^k+C, Acta Math. Hungar., 149 (1), 190-207, 2016 | | Lapkova, K.: Explicit upper bound for an average number of divisors of quadratic polynomials, Arch. Math. (Basel) 106, no. 3, 247-256, 2016 | | Keleti T., Matolcsi M., Oliveira Filho, F. M., Ruzsa I. Z.: Better bounds for planar sets avoiding unit distances, Discrete & Computational Geometry 55 (3), 642-661, 2016 | | Bárány I., Solymosi J.: Gershgorin disks for multiple eigenvalues of non-negative matrices, A Journey Through Discrete Mathematics, A Tribute to Jiří Matoušek Eds. Loebl, M., Nešetřil, J., Thomas, R., Springer, 2017 | | Solymosi J., Ching Wong: Cycles in graphs of fixed girth with large size, European Journal of Combinatorics 62, May, 124-131, 2017 | | Ellenberg, J. S., Solymosi, J., Zahl, J.: New bounds on curve tangencies and orthogonalities, Discrete Analysis 18, 22 pp., 2016 | | Solymosi D., Solymosi J.: Small cores in 3-uniform hypergraphs, Journal of Combinatorial Theory, Series B, Volume 122, January, 897-910, 2017 | | Solymosi, J., de Zeeuw, F.: Incidence bounds for complex algebraic curves on Cartesian products, New Trends in Intuitive Geometry, Bolyai Soc. Math. Studies, Ambrus G. et al. eds., Springer, 2017 | | Balog, A., Shakan, G.: On the sum of dilations of a set, Acta Arithmetica, 164, 153-162, 2014 | | Balog, A., Rochet-Newton, O.: New sum-product estimates for real and complex numbers, Discrete and Computational Geometry 53, 825-846, 2015 | | Balog, A., Shakan, G.: Sum of dilates in vector spaces, North-Western European Journal of Mathematics 1, 46-54, 2015 | | Balog, A., Wooley, T. D.: A low-energy decomposition theorem, Advance Access in Quart. J. of Math., Oxford, 2016 | | Balog A., Rivat J., Sárközy A.: On arithmetic properties of sumsets, Acta Math. Hungar. 144 (1), 18-42, 2014 | | Gyarmati, K., Mauduit, C., Sárközy A.: On finite pseudorandom binary lattices, J. Applied Discrete Math. 216 (3), 589-597, 2017 | | Dartyge, C., Gyarmati, K., Sárközy A.: On irregularities of distribution of binary sequences relative to arithmetic progressions, II (Special sequences), Unif. Distr. Theory, to appear, 2017 | | Révész Sz. Gy.: A discrete extension of the Blaschke rolling ball theorem, Geom Dedicata 182: 51–72., 2016 | | Blomer, V. Harcos, G. Maga, P., Milicevic, D.: The sup-norm problem for GL(2) over number fields, to appear, 2017 | | Blomer, V. Harcos, G., Milicevic, D.: Bounds for eigenforms on arithmetic hyperbolic 3-manifolds, Duke Math. J. 165, 625-659, 2016 | | Pintz J.: Distribution of Zeta Zeros and the Osclllation of the Error Term of the Prime Number Theorem, Festschrift for the 125th anniversary of the birth of I. M. Vinogradov, Proc. Of the Steklov Institute, to appear, 2017 | | Pintz J.: Patterns of primes in arithmetic progressions, Number Theory – Diophantine Problems, Uniform Distribution and Applications, Festschrift in Honour of Robert F. Tichy, Eds. Ch. Elsholtz, P. Grabner, Springer, to appear, 2017 | | Huszti A., Oláh N.: A Simple Authentication Scheme for Clouds, IEEE Conference on Communications and Network Security, 2nd workshop on Security and Privacy in the Cloud (SPC 2016), to appear, 2017 | | Bérczes A., Dujella A., Hajdu L., Tengely Sz.: Finiteness results for F-Diophantine sets, Monatshefte für Mathematik, 180: 469–484, 2016 | | Bérczes A., Luca F., Pink I., Ziegler V.: Finiteness results for Diophantine triples with repdigit values, Acta Arithmetica, 172: 133–148, 2016 | | Bérczes, A., Hajdu, L., Miyazaki, T., Pink, I.: On the equation 1^k+2^k+…+x^k=y^n for fixed x, J. Number Theory 163: 43-60, 2016 | | Bérczes, A., Hajdu, L., Miyazaki, T., Pink, I.: On the Diophantine equation 1+x^a+z^b=y^n, Journal of Combinatorics and Number Theory 8, 145-154, 2016 | | Bérczes, A., Bilu, Y., Luca, F.: Diophantine equations with products of consecutive members of binary recurrences, Ramanujan J., to appear, 2016 | | Bérczes A., Luca F., Pink I., Ziegler V.: On trinomials with integral S-unit coefficients having a quadratic factor, to appear, 2017 | | Pintér Á., Rakaczki Cs.: On the decomposability of linear combinations of Bernoulli polynomials, Monatshefte Math. 180, 631-648, 2016 | | Evertse, J. H., Győry, K.: Discriminant equations in diophantine number theory, Cambridge University Press, 2016 | | Győry, K.: On some norm inequalities and discriminant inequalities in CM-fields, Publ. Math. 89, 513-523, 2016 | | Evertse, J. H., Győry, K.: Effective results for discriminant equations over finitely generated domains, Number Theory - Diophantine problems, Uniform distribution and applications, to appear, 2017 | | Hajdu, L., Laishram, S., Tengely, Sz.: Power values of sums of products of consecutive integers, Acta Arith. 172, 333-349, 2016 | | Bertók Cs., Hajdu L., Pethő A.: On the distribution of polynomials with bounded height, Publ. Math., to appear, 2017 | | Akiyama, S., Evertse, J.-H., Pethő, A.: On nearly linear recurrence sequences, Number Theory - Diophantine problems, Uniform Distribution and Applications - Festschrift in Honour of Robert F. Tichy's 60th Birthday, Eds.: Elsholtz, Grabner, 2017 | | Komornik, V., Pedicini, M., Pethő, A.: Multiple common expansions in non-integer bases, Acta Sci. Math. (Szeged), to appear, 2017 | | Bazsó A., Mező I.: On the coefficients of polynomials related to alternating power sums of arithmetic progressions, to appear, 2017 | | Katona Gy. O. H.: Around the Complete Intersection Theorem, Discrete Applied Mathematics 216 (3), 618-621, 2017 | | Ruzsa I. Z.: Exact additive complements, Quart. J. Math. Oxford, to appear, 2017 | | Bérczes A., Dujella A., Hajdu A., Tengely Sz.: Finiteness results for F-Diophantine sets, Mh. Math., to appear, 2016 | | Bérczes A., Luca F., Pink I., Ziegler V.: Finiteness results for Diophantine triples with repdigit values, Acta Arith., to appear, 2016 | | Bérczes A., Hajdu L. Miyazaki T., Pink I.: On the equation 1^k+2^k+...x^k=y^n for fixed x, J. Number Theory, to appear, 2016 | | Evertse, J.H., Győry, K.: Discriminant Equations in Diophantine Number theory, Cambridge University Press, to appear, 2016 | | Huszti, A.: Analyzing security requirements for cryptographic protocols, Thesis for Habilitation, Debrecen Univ., 2015 | | Akiyama, S., Pethő, A.,: On the distribution of polynomials with bounded roots, II, Polynomial with integer coefficients, Unif. Distrib. Theory 9, 5-19., 2014 | | Ádámkó, É., Pethő, A.: Location-stamp for GPS coordinates, Acta Univ. Sap., Informatica 5, 63-76., 2013 | | Aszalós, L., Hajdu, L., Pethő A.,: On a correlational clustering of integers, Indag. Math. , to appear, 2015 | | Pethő, A., Varga, P., Weitzer, M.: On Shift Radix Systems over Imaginary Quadratic Euclidean Domains, Acta Cybernetica 22, 485-498., 2015 | | Pethő A., Varga, P.,: Canonical number systems over imaginary quadratic Euclidean domains, Colloq. Math., to appear, 2016 | | Tengely, Sz.: On the Lucas sequence, Periodica Math. Hung. 71 (2), 236-242., 2015 | | Tengely, Sz.: On a peoblem of Erdős and Graham, Periodica Math. Hung., to appear, 2016 | | A., Hajdu, L.,Laishram,S., Tengely, Sz.: Power values of sums of products of consecutive integers, Acta Arith., to appear, 2016 | | Tengely, Sz., Varga, N.: Rational function variant of a problem of Erdős and Graham, Glasnik Matematicki 50 (1), 65-76., 2015 | | D. Kaptan: A note on small gaps between primes in arithmetic progressions, Acta Arith., to appear, 2016 | | D. A. Kaptan: A note on small gaps between primes in arithmetic progressions, Acta Arith., to appear, 2016 | | V. Blomer, P. Maga: Subconvexity for sup-norms of cusp forms on PGL(4), Selecta Math., to appear, 2016 | | G. Harcos, M. Iazzi, Y.-H. Liu, M. Troyer, L. Wang: Split orthogonal group: A guiding principle for sign-problem-free fermonic simulations, Phys. Rev. Lett. 115, no. 25, Art ID 250601, 6 pp., 2015 | | G. Harcos: Prímek, Polignac, Polymath, Mat. Lapok (N:S.) 20, no.2, 1-13., 2014 | | V. Blomer, G. Harcos, D. Milicevic: Bounds for eigenforms on arithmetic hyperbolic 3-manifolds, Duke Math. J., to appear, 2016 | | A. Birő, K. Lapkova: The class number one problem for the real quadratic fields Q(sqrt{an^2+4a}), Acta Arith. 172, no.2, 117-131., 2016 | | S. Krenedits, Sz. Gyí. Révész: Carathéodory-Fejér type extremal problems on locally compact groups, J. Approx. Théory 194, 108-131., 2015 | | A. G. Babenko, M.V. Deikalova, Sz. G. Révész: Weighted one-sided approximation of characteristic functions of intervals by polynomials on a closed interval, Proc. Steklov Institute of Mathematics (Supplementary Issues) 21, 46-53., 2015 | | A. Balog, A. Granville, J. Solymosi: Gaps between fractional parts, and additive combinatorics, The Quarterly Journal of Mathematics hav012, 2015 | | O.E. Raz, M. Sharir, J. Solymosi: On Triple Intersections of Three Families of Unit Circles, Discrete and Computational Geometry 54, no.4, 2015 | | O. E. Raz, M. Sharir, J. Solymosi: Polynomials vanishing on grids: The Elekes_Ronyai problem revisited, Amer. J. Math., to appear, 2016 | | A. Granville, J. Solymosi: Sum-Product formulae, Recent Trends in Combinatorics, the ImA Volumes in Mathematics and its Applications 159 (Eds. A. Beveridge et al.), Springer International Publishing, Switzerland, to app, 2016 | | Gyarmati, K., Sárközy, A.: On reducible and primitive subsets of F_p, Integers (EJCNT) 15A, No. A6, 21 pp., 2015 | | C. Dartyge, K. Gyarmati, A. Sárközy: On irregularities of distribution of sequences relative to arithmetic progressions I. (General results), Unif. Distrib. Theory, to appear, 2016 | | K. Gyarmati, A. Sárközy: On reducible and primitive subsets of F_p, II, Quart. J. Math. Oxford, to appear, 2016 | | C. Mauduit, J. Rivat, A. Sárközy: On the difits of sumsets, Canadian J. Math., to appear, 2016 | | K. Gyarmati, C. Mauduit, A. Sárközy: Generation of further pseudorandom binary sequences, I (Blowing up a single sequence),, Unif. Distr: Theory 10 , 35-61., 2015 | | J. Pintz: An approximation to the twin priome conjecture and the parity phenomenon, Indag. Math. 26, 883-896., 2015 | | J. Pintz: Polignac numbers, Conjecture of Erdős on Gaps between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture,, in: From Arithmetic to Zeta-Functions - Number Theory on Memory of Wolfgang Schwarz, Eds. J. Sander, J. Steuding, R. Steuding, Springer, to appear, 2016 | | F. Bayart, I.Z.Ruzsa: Difference sets and frequently hyperweighted shifts, Ergodic Theory and Dynamical Systems 35 (3), 691-709, 2015 | | G. Harcos: Twisted Hilbert modular L-functions and spectral theory, Proc. CIMPA-UNESCO-CHINA Research School, 2014 | | R. Schwartz, J. Solymosi: Combinatorial applications of the subspace theorem,, Geometry, Structure and Randomness in Combinatorics, Edizioni della Normale di Pisa, 2014 | | O.E. Raz, M. Sharir, J. Solymosi: On triple intersections of three families of unit circles,, ACM, The 30th Annual Symposium on Computational Geometry (SoCG 2014), 2014 | | O. E. Raz, M. Sharir, J. Solymosi: Polynomials vanishing on grids: The Elekes-Rónyai problem revisited, ACM, The 30th Annual symposium on Computational Geometry (SoCG 2014), 2014 | | M. Sharir, A. Scheffer, J. Solymosi: Distinct distances on two lines, J. Comb. Theory, Ser. A. 120 (2013), No. 7, 1732-1736, 2013 | | A. Balog, J. Rivat, A. Sárközy: On arithmetic properties of sumsets, Acta Math. Hungar. Acad. Sci., 2014 | | J. Pintz: Paul Erdős and the difference of primes, Erdős Centennial, Bolyai Soc. Math. Stud. , Vol. 25, Springer, pp. 485-513, 2013 | | J. Pintz: The twin prime conjecture, Bonded gaps between consecutive primes, and Polignac numbers, Eureka, The Archimedian Journal, 2014 | | B. Farkas, J. Pintz, Sz. Gy. Révész: On the optimal weight function in the Goldston-Pintz-Yildirm method for finding small gaps between consecutive primes, Number theory, Analysis, and Combinatorics, Proceedings of the Paul Turán Memorial conference held Augiust 22-26, 2011 in Budapest, de Gruyter, Berlin, pp. 75-104, 2014 | | J. Pintz: Some new results on small gaps between consecutive primes, Number theory, Analysis, and Combinatorics, Proceedings of the Paul Turán Memorial conference held Augiust 22-26, 2011 in Budapest, de Gruyter, Berlin, pP. 261-278., 2014 | | A. Sárközy: On multiplicative decompositions of the set of shifted quadratic residues modulo p, Number theory, Analysis, and Combinatorics, Proceedings of the Paul Turán Memorial conference held Augiust 22-26, 2011 in Budapest, de Gruyter, Berlin, pp. 295-307, 2014 | | K. Gyarmati, C. Mauduit, A. Sárközy: On linear complexity of binary lattices, II,, Ramanujan J., 2014 | | K. Gyarmati, C. Mauduit, A. Sárközy: The cross-relation measure for families of binary sequences, Applications of Algebra and Number Theory (Lectures on the Occasion of Harald Niederreiter's 70th Birthday, 2014 | | K. Gyarmati, A. Sárközy: On reducible and primitive subsets of F_p, Integers (EJCNT), 2014 | | Schwartz R; Solymosi J: Combinatorial applications of the subspace theorem, pp 123-140 in: Geometry, Structure and Randomness in Combinatorics, Scuola Normale Superiore, 2014 | | Akiyama S; Pethő A: On the distribution of polynomials with bounded roots I. Polynomials with real coefficients, J Math Soc Japan 66: 927-949, 2014 | | Raz OE; Sharir M; Solymosi J: Polynomials vanishing on grids: The Elekes--Rónyai problem revisited, pp 251-260 in: The 30th Ann Symp on Comp Geometry (SoCG 2014), ACM Press, New York, 2014 | | Raz OE; Sharir M; Solymosi J: On triple intersections of three families of unit circles, pp 198-205 in: The 30th Ann Symp on Comp Geometry (SoCG 2014), ACM Press, New York, 2014 | | Hajdu L; Kovács T; Pethő A; Pohst M: An optimization problem for lattices, Experimental Math 22: 4, 443-455, 2013 | | Pethő A; Tengely Sz: On composite rational functions, pp 241-259 in: Number theory, analysis, and combinatorics, De Gruyter, Berlin, 2014 | | Hirata-Kohno N; Pethő A: On a key exchange protocol based on Diophantine equations, Infocommunications Journal 5: 17-21, 2013 | | Komornik V; Pethő A: Common expansions in noninteger bases, Publ Math Debrecen 85: 489-501, 2014 | | Akiyama S; Brunotte H; Pethő A; Steiner W; Thuswaldner AJ: Problems and conjectures around shift radix systems, Open Problems in Mathematics Vol 2, 2014 | | Bérczes A; Pethő A: On the sumset of binary recurrence sequences, Publ Math Debrecen 84: 279-290, 2014 | | Bérczes A; Hajdu L; Hirata-Kohno N; Kovács T; Pethő A: A key exchange protocol based on Diophantine equations and S-integers, JSIAM Letters 6: 85-88, 2014 | | Akiyama S; Aszalós L; Hajdu L; Pethő A: Correlation Clustering of Graphs and Integers, Infocommunications journal 6: 3-12., 2014 | | Győry K; Kovács T; Péter Gy; Pintér Á: Equal values of standard counting polinomials, Publ Math Debrecen 84: 259-277, 2014 | | Bérczes A; Evertse JH; Győry K: Effective results for Diophantine equations over finitely generated domains, Acta Arith 163: 71-100, 2014 | | Győry K; Hajdu L; Tijdeman R: Representation of finite graphs os difference graphs of S-units, I, J Comb Theory A 127: 314-335, 2014 | | Evertse JH; Győry K: Unit Equations in Diophantine Number Theory, Cambridge University Press, megjelenőben, 2015 | | Bennett MA; Pintér Á: Intersections of recurrence sequences, Proc Amer Math Soc, megjelenőben, 2015 | | He Bo; Pintér Á; Togbé A; Varga N: A generalization of a problem of Mordell, Glasnik Matematicki, megjelenőben, 2015 | | He Bo; Pintér Á; Togbé A: On simultaneous Pell equation and related Thue equations, Proc Amer Math Soc, megjelenőben, 2015 | | Győry K; Kovács T; Péter Gy; Pintér Á: Equal values of standard counting polynomials, Publ Math Debrecen 84: (1-2) 259-277, 2014 | | Hajdu L; Pintér Á; Tengely Sz; Varga N: Equal values of figurate numbers, Journal of Number Theory 137: 130-141, 2014 | | Bilu YF; Fuchs C; Luca F; Pintér Á: Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations, Publ Math Debrecen 82: (1) 219-254, 2013 | | He Bo; Pink I; Pintér Á; Togbé A: On the diophantine inequality |X^2-cXY^2+Y^4|<=c+2, Glasnik Matematicki 48: (2) 291-299, 2013 | | Kim D; Park YK; Pintér Á: A diophantine problem oncerning polygonal numbers, Bull Australian Math Soc 88: (2) 345-350, 2013 | | Pintér Á; Srivastava HM: Addition theorems for the Appell polynomials and the associated classes of polynomial expansions, Aequationes Math 85: (3) 483-495, 2013 | | Tengely Sz; Varga N: On a generalization of a problem of Erdős and Graham, Publ. Math. Debrecen 84: (3-4) 475-482, 2014 | | Pintér Á; Tengely Sz: The Korteweg--de Vries equation and a Diophantine problem related to Bernoulli polynomials, Advances in Difference Equations 2013 (1) Paper 245, 1-9, 2013 | | Bazsó A: On alternating power sums of arithmetic progressions, Integral Transforms and Special Functions 24: (12) 945-949, 2013 | | Bazsó A; Pink I: Diophantine equations with Appell sequences, Periodica Mathematica Hungarica 69: 222-230, 2014 | | Huszti A; Kovács Z: Bilinear Pairing-based Hybrid Mixnet with Anonymity Revocation, in: Proceedings of ICISSP 2015, SCITEPRESS, 2015 | | Huszti A: Anonymous Multi-Vendor Micropayment Scheme based on Bilinear Maps, pp 27-32 in: Proceedings of the International Conference on Information Society, IEEE Press, 2014 | | Huszti A: Multi-Vendor PayWord with Payment Approval, pp 265-271 in: Proc 2013 Intern Conf on SAM, CSREA Press, 2013 | | Bérczes A; Ziegler V: On geometric progressions on Pell equations and Lucas sequences, Glasnik Matematicki 48: 1-22, 2013 | | Bérczes A; Dujella A; Hajdu L: The sequence of S-units, J. Number Theory 138: 48-68, 2014 | | Bérczes A; Pink I: On generalized Lebesgue--Ramanujan--Nagell equations, An. St. Univ. Ovidius Constanţa 22: 51-71., 2014 | | Bérczes A; Evertse JH; Győry K: Effective results for Diophantine equations over finitely generated domains, Acta Arithmetica 163: 71-100, 2014 | | Bérczes A; Ziegler V: On simultaneous palindromes, Journal of Combinatorics and Number Theory 6: no 1, 2014 | | Bérczes A: Effective results for unit points on curves over finitely generated domains, Math Proc Cambridge Phil Soc 158: 331–353, 2015 | | Bérczes A: Effective results for division points on curves in G_m^2, J Théor Nombres Bordeaux, submitted, 2015 | | Hirata-Kohno N; Kovács T: Computing S-integral points on elliptic curves of rank at least 3, pp 92-102 in: RIMS Kokyuroku 1898, Analytic Number Theory, Res Inst Math Sci Kyoto Univ, Kyoto, Japan, 2014 | | Kovács T; Rábai Zs: Equal values of pyramidal numbers, közlésre benyújtva, 2015 | | Hirata-Kohno N; Kovács T: S-integral points on elliptic curves via new approximation of p-adic elliptic logarithms, közlésre benyújtva, 2015 | | Hirata-Kohno N; Kovács T; Miyazaki T: On the Nagell--Ljunggren-equation, közlésre előkészítve, 2015 | | Biro A: An identity related to Wilson functions, Acta Mathematica Hungarica 144: (2) 367-406, 2014 | | Raz OE; Sharir M; Solymosi J: Polynomials vanishing on grids: The Elekes--Rónyai problem revisited, American Journal of Mathematics, megjelenőben, 2015 | | Sharir M; Solymosi J: Distinct distances from three points, Combinatorics, Probability and Computing, megjelenőben, 2015 | | Solymosi J: The (7, 4)-Conjecture in Finite Groups, Probability and Computing, accepted, available on CJO2015. doi:10.1017/S0963548314000856, 2015 | | Farkas B; Révész SzGy: The periodic decomposition problem, pp 143-170 in: Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer-Verlag, Berlin--Heidelberg, 2014 | | Bachoc C; Matolcsi M; Ruzsa IZ: Squares and difference sets in finite fields, Integers, Vol. 13, Article A77, 2013 | | Malikiosis RD; Matolcsi M; Ruzsa IZ: A note on the pyjama problem, Eur J Comb 34: (7) 1071-1077, 2013 | | Matolcsi M; Ruzsa IZ; Weiner M: Systems of mutually unbiased Hadamard matrices containing real and complex matrices, Australasian J. Combinatorics 55: 35-47, 2013 | | Matolcsi M; Ruzsa IZ: Sets with no solutions to x+y=3z, European J Combin 34: (8) 1411-1414, 2013 | | Keleti T; Matolcsi M; de Oliveira Filho FM; Ruzsa IZ: Better bounds for planar sets avoiding unit distances, submitted for publication, 2015 | | Gyarmati K: On the complexity of a family of Legendre sequences with irreducible polynomials, Finite Fields and Their Applications 33: 175-186, 2015 | | Gyarmati K; Mauduit C; Sárközy A: Generation of further pseudorandom binary sequences, I (Blowing up a single sequence), Uniform Distribution Theory 10: (1) 35-61, 2015 | | POLYMATH DHJ (Castryck W; Fouvry É; Harcos G; Kowalski E; Michel P; Nelson P; Paldi E; Pintz J; et al): Variants of the Selberg sieve, and bounded intervals containing many primes, Res. Math. Sci. 1: (12) 83 pp, 2014 | | POLYMATH DHJ (Castryck W; Fouvry É; Harcos G; Kowalski E; Michel P; Nelson P; Paldi E; Pintz J; et al): New equidistribution estimates of Zhang type, Algebra & Number Theory 8: 2067-2199, 2014 | | Harcos G: Primek, Polignac, Polymath, Mat. Lapok (N.S.) megjelenés alatt, 2015 | | Kaptan DA: A generalization of the Goldston--Pintz--Yildirim prime gaps result to number fields, Acta Math Hungar 141: (1-2) 84-112, 2013 | | Kaptan DA: Erratum to: "A generalization of the Goldston--Pintz--Yildirim prime gaps result to number fields'', Acta Math Hungar 144: (2) 530., 2014 | | Blomer V; Maga P: The sup-norm problem for PGL(4), Int Math Res Not, megjelenőben, 2015 | | Blomer V; Maga P: Subconvexity for the sup-norms of automorphic forms on PGL(n), submitted, 2015 | | Bollobás B; Füredi Z; Kantor I; Katona GOH; Leader I: A coding problem for pairs of subsets, pp 47-58 in: Geometry, Structure and Randomness in Combinatorics, Edizioni Della Normale, CRM Series 18, 2015 | | Katona GOH; Nagy DT: Incomparable copies of a poset in the Boolean lattice, Order, megjelenőben, 2015 | | Katona GOH; Nagy DT: Union-intersecting set sytems, Graphs and Combinatorics, megjelenőben, 2015 | | Bérczes A; Evertse JH; Győry K: Multiply monogenic orders, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 12: 467-497, 2013 | | Bérczes A; Luca F: On the sum of digits of numerators of Bernoulli numbers, Canad Math Bull; 56: 723-728, 2013 | | Bérczes A; Evertse JH; Győry K: Effective results for hyper- and superelliptic equations over number fields, Publ Math Debrecen 82: 727-756, 2013 | | Schwartz R; Solymosi J; de Zeeuw F: Extensions of a result of Elekes and Rónyai, Journal of Combinatorial Theory - Series A 120: 1695-1713, Academic Press, 2013 | | Simonovits M: Paul Erdős in the 21st century, Journal of the European Mathematical Society 91: 23-29, 2014 | | Goldston DA; Pintz J; Yildirim CY: Small gaps between primes, pp 419-441 in: ICM Proceedings, Soeul 2014, IMU, 2014 | | Füredi Z; Simonovits M: The history of degenerate (bipartite extremal) problems, pp 169-264 in: Bolyai Soc Math Studies 25 J Bolyai Math Soc and Springer, Budapest and Berlin-Heidelbeg-New York, 2013 | | Simonovits M: Paul Turán's influence in combinatorics, pp 309-392 in: Number Theory, Analysis, and Combinatorics, Walter de Gruyter, Berlin--Boston, 2014 | | Szemerédi E: Is laziness paying off? ("Absorbing method"), pp 17-34 in: Colloquia de Giorgi 2010-2012, vol 4, Springer, Berlin--Heidelberg--New York, 2013 | | Matolcsi M; Ruzsa IZ: Difference sets and positive exponential sums I. General properties, J Fourier Anal Appl 20: (1) 17-41, 2014 | | K. Gyarmati, C. Mauduit, A. Sárközy: On linear complexity of binary lattices, II,, Ramanujan J. 34 (2), 237-263., 2014 | | K. Gyarmati, C. Mauduit, A. Sárközy: The cross-relation measure for families of binary sequences, Applications of Algebra and Number Theory (Lectures on the Occasion of Harald Niederreiter's 70th Birthday), (Eds. G. larcher et al.), Cambridge Univ. Press, pp. 126-143, 2014 | | Evertse JH; Győry K: Unit Equations in Diophantine Number Theory, Cambridge University Press, 2015 | | Bennett MA; Pintér Á: Intersections of recurrence sequences, Proc Amer Math Soc. 143, 2347-2353, 2015 | | He Bo; Pintér Á; Togbé A; Varga N: A generalization of a problem of Mordell, Glasnik Matematicki, 50(1) 35-41., 2015 | | He Bo; Pintér Á; Togbé A: On simultaneous Pell equation and related Thue equations, Proc Amer Math Soc, 143, 4685-4693., 2015 | | Huszti A; Kovács Z: Bilinear Pairing-based Hybrid Mixnet with Anonymity Revocation, in: Proceedings of ICISSP 2015, SCITEPRESS, pp. 238-245., 2015 | | Bérczes A: Effective results for division points on curves in G_m^2, J Théor Nombres Bordeaux,27, 405-437, 2015 | | Solymosi J: The (7, 4)-Conjecture in Finite Groups, Combinatorics, Probability and Computing 24 (04), 680-686., 2015 | | Keleti T; Matolcsi M; de Oliveira Filho FM; Ruzsa IZ: Better bounds for planar sets avoiding unit distances, Discrete and Computational Geometry, to appear, 2016 | | Blomer V; Maga P: The sup-norm problem for PGL(4), Int Math Res Not. 14, 5311-5332., 2015 | | Blomer V; Maga P: Subconvexity for sup-norms of cusp forms on PGL(n), Selecta Math., 2016 | | Bazsó, A., Mező, I.: On the coefficients of power sums of arithmetic progressions, J. Number Theory153, 117-123., 2015 | | Bazső, A.: Polynomial values of (alternating) power sums, Acta Math. Hungar. 146, 202-219., 2015 | | Bérczes, A., Pethő, A.: On the sumset of Lucas sequences, Publ.Math. Debrecen, 84, 279-290., 2014 |
|
|
|
|
|
|
|
|
|
