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Details of project

  
Identifier
100291
Type K
Principal investigator Sárközy, András
Title in Hungarian Analitikus, kombinatorikus es szamitogepes szamelmelet
Title in English Analytical, combinatorial and computational number theory
Keywords in Hungarian szamelmelet, szamitogepes szamelmelet
Keywords in English number theory, computational number theory
Discipline
Mathematics (Council of Physical Sciences)100 %
Ortelius classification: Number theory
Panel Mathematics and Computing Science
Department or equivalent Department of Algebra and Number Theory (Eötvös Loránd University)
Participants Biró, András
Borbély, József
Gyarmati, Katalin
Hegyvári, Norbert
Károlyi, Gyula
Mérai, László
Pintz, János
Szalay, Mihály
Zábrádi, Gergely
Starting date 2012-01-01
Closing date 2016-12-31
Funding (in million HUF) 17.209
FTE (full time equivalent) 18.78
state closed project
Summary in Hungarian
A pályázat célja a Turán Pál és Erdős Pál által alapított analitikus és kombinatorikus iskola keretében végzett, főként az ELTE Algebra és Számelmélet Tanszékére épülő kutatás eredményes folytatásához szükséges támogatás biztosítása. E kutatást támogatta korábban a T43623 számú OTKA program (2003-2007; ennek keretében 86 cikk született, melyek általában rangos nemzetközi folyóiratban jelentek meg), és idén junius 30-án zárul a K67676 számú OTKA program (2007-2011; ennek első 3 évében 60 cikk készült el.) Az új pályázat keretében is folytatni szándékozunk olyan korábbi témák kutatását, mint analitikus primszámelmélet; particiók; sorozatok additív és multiplikatív tulajdonságai; sorozatok eloszlásának egyenletessége illetve irregularitásai, diszkrepancia kérdések. A közelmúltban kezdtük a munkát néhány új területen: pszeudovéletlen struktúrák; karakterösszegek becslése; algebrai számelmélet; algebrai módszerek a kombinatórikus számelméletben; algebrai egyenletek megoldásainak vizsgálata véges testekben; e kutatások folytatását tervezzük. Lesznek új témák is: kis primfaktorokból felépülő számokra vonatkozó kérdések; automorf formák vizsgálata; aritmetikai algebrai geometriai vizsgálatok.

Megjegyzés: Az FTE korlátra tekintettel Bíró András csak 2013 január 1 -től vesz részt a kutatásban.
Summary
The aim of the grant application is to ensure the financial support needed for the successful continuation of the research carried out in frame of an analytical and combinatorial number theory school founded by Paul Turán and Paul Erdős and based mostly on the Algebra and Number Theory Department of the Eötvös Loránd University. This research was supported earlier by OTKA program no. T43623 (2003-2007; during this program 86 papers were written, published mostly in strong international journals) and by the OTKA program no. K67676 ending in June this year (2007-2011; in the first 3 years of this program 60 papers have been published). In the new program we would like to continue the research initiated earlier in the following fields: analytical number theory; partitions; additive and multiplicative properties of sequences of integers; uniformity, resp. irregularities of distribution of sequences, discrepancy problems. Recently we have started the work in some further fields: pseudorandom structures; estimates of character sums; algebraic number theory; algebraic methods in combinatotrial number theory; study of solutions of algebraic equations in finite fields. We would like to continue and extend the research in these new fields. There will be also new subjects to be studied: problems on integers composed of "small" primes; study of automorphic forms; problems in arithmetic algebraic number theory.

Remark: In view of the FTE restrictions András Bíró joins the research only on January 1, 2013.




 

Final report

  
Results in Hungarian
E kutatás keretében a kutató csoport tagjai összesen 73 cikket publikáltak. Valamennyi cikk angol nyelvű, és általában rangos nemzetközi folyóiratokban jelentek meg. E cikkek témáját ismertettük az előző részjelentésekben, illetve e beszámolóhoz kapcsolt fileban . Különösen kiemelkedőek a Pintz által a primszámelméletben, Gayarmati, Mérai és Sárközy által a pszeudovéletlenség elméletében, valamint a Gyarmati, Sárközy, Hegyvári és Szalay által az additív számelméletben elért eredmények (melyeknek akár csak vázlatos ismertetésére sincs itt lehetőség a korlátozott terjedelem miatt).
Results in English
During this research the members of the team published altogether 73 research papers. Each of the papers is of English language, and in general they appeared in strong international journals. The subjects of these have been described in the earlier reports and in the file attached to this report, respectively. Especially important results have been proved in prime number theory in Pintz, in the theory of pseudorandomness by Gyarmati, Mérai and Sárközy, and in additive number theory by Gyarmati, Sárközy, Hegyvári and Szalay (a detailed report of these results can not be presented here because of the restricted extent of this report)..
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=100291
Decision
Yes





 

List of publications

  
Hegyvári N., Hennecart F: On the distribution of the values of multivariate rational functions, Uniform Distribution Theory 9(2): 103-123, 2014
Mérai L.: On the typical values of the cross-correlation measure, Monatshefte Math. 180(1): 83-99, 2016
Sárközy A.: On pseudorandomness of families of binary sequences, J. Applied Discrete Math. 216(3): 670-676, 2017
Gyarmati K., Mauduit C., Sárközy A.: On finite pseudorandom binary lattices, J. Applied Discrete Math. 216(3): 589-597, 2017
Erdélyi M., Zábrádi G.: Links between generalized Montréal functors, Math. Zeitschrift (közlésre elfogadva), 2014
Károlyi Gy, Komjáth P: Well ordering groups with no monotone arithmetic progressions, Order (közlésre elfogadva), 2015
Dartyge C.; Szalay M.: On a phenomenon of Turán concerning the summands of partitiona, Acta Math. Hungar. 149(2): 375-395, 2016
Mérai L.: The cross-correlation measure of families of finite binary sequences: limiting distributions and minimal values, Discrete Applied Math. 214: 153-168, 2016
Mérai L.; Winterhof A.: On the linear complexity profile of some sequences derived from elliptic curves, Des. Codes Cryptogr. 81(2): 259-267, 2016
Zábrádi G.: Multivariate (phi,gamma)-modules and smooth o-torsion representations, Selecta Math. (közlésre elfogadtva), 2016
Hegyvári N.: On deterministic and random rolling of polyhedra, Int.Electron. J. Geom. 9(1): 85-88, 2016
Dartyge C., Gyarmati K., Sárközy A.: On iiregularities of distribution of binary sequences relative to arithmetic progressions, II (Special sequences), Unif. Distr. Theory (közlésre benyujtva), 2016
Zábrádi G.: Multivariable (phi.Gamma)-modules and product of Galois groups, Math. Research Letters (közlésre benyujtva), 2016
Szamuely T; Zábrádi G: The p-adic Hodge decomposition according to Beilinson, Procof the 2015 AMS Summer Institute in Algebraic Geomettry (közlésre elfogadva), 2016
Csapodi C; Hegyvári N: On some irrational decimal fractions, revisited, Elemente Math. (közlésre benyujtva), 2016
Hegyvári N; Hennecart F;: A note on the set A+A^2, Ramanujan J. (közlésre benyujtva), 2016
Pintz J.: Distribution of zeta zeros and the oscillation 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 (közlésre elfogadva), 2016
Pintz J.: Patterns of primes in arithmetic progressions, Number Theory - Diophantine Problems, Uniform Distribution and Applications, Festschrift in Honour of R. F. Tichy, eds. C. Elsholtz et al., Springer (közlésre elfogadva), 2016
Hegyvári N.: Note on character sums of Hilbert cubes, J. Number Theory 160: 526-535, 2016
Hegyvári N; Ruzsa I. Z.: Additive structure of difference sets and a theorem of Folner, Australian J. Combinatorics 64: 437-443, 2016
Gyarmati K: Measures of pseudorandomness,, Finite fields and applications: character sums and polynomials, eds. P. Charpin et al.,Random Series in Computational and applied Math., de Gruyter, 43-64, 2013
Dartyge C; Mauduit C; Sárközy A: Values of polynomials and generators with "missing digits" in finite fields, Funct. Approx. Comment. Math. (közlésre elfogadva), 2013
Gyarmati K; Konyagin S; Sárközy A: On the reducibility of large sets of residues modulo p, J. Number Theory 133(7): 2374-2397, 2013
Gyarmati K; Mauduit C; Sárközy A: On linear complexity of binary lattices, II, Ramanujan J. (közlésre elfogadva), 2013
Mauduit C; Sárközy A: Family complexity and VC-dimension, Ahlswede Festschrift, eds. H. Aydinian et al., LNCS 7777, Springer, Berlin, 346-363, 2013
Goldston DA; Pintz J; Yildirim CY: Primes in tuples IV: Density of small gaps between consecutive primes, Acta Arith. 160: 37-53, 2013
Pintz J: The bounded gap conjecture and bounds between consecutive Goldbach numbers, Acta Arith. 155: 297-305, 2012
Hegyvári N; Hennecart F: Conditional expanding bounds for two-variable functions over prime fields, Europ. J. Combin. 34: 1365-1382, 2013
Hegyvári N; Hennecart F: Structure of product set in the Heisenberg groups, Moscow J. Combin. Number Th. 3: 57-69, 2013
Károlyi Gy; Paulin R: On the exterior algebra method applied to restriscted set addition, European J. Combin. 34: 1383-1389, 2013
Károlyi Gy; Lascoux A; Warnaar SO: Constant term identities and Poincare polynomials, Trans. Amer. Math. Soc. (közlésre elküldve), 2013
Károlyi Gy: A Lie algebra approach to difference sets, Annales Univ. Sci. Budapest. Eötvös (közlésre elküldve), 2013
Mérai L: The higher dimensional analogue of certain estimates of Roth and Sárközy, Periodica Math. Hungar. (közlésre elfogadva), 2013
Schneider P; Vigneras MF; Zábrádi G: From étale P_+ representations to G equivariant sheaves on G/P, in Proc. LMS Durham Symposium on Automorphic Forms and Galois Representations, London Math. Soc. Lecture Notes Series (közlésre elfofadva), 2013
Zábrádi G: (phi,gamma)-modules over noncommutative overconvergent and Robba rings, J. Algebra Number Th. (közlésre beküldve), 2013
Sárközy A: On multiplicative decompositions of the set of the shifted quadratic residues modulo p, Number Theory, Analysis and Combinatorics, W. De Gruyter, Berlin, 295-306, 2013
Gyarmati K; Mauduit C; Sárközy A: The cross-correlation measure for families of binary sequences, Applications of Algebra and Number Theory (Lectures on the Occasion of Harald Niederreiter's 70th Birthday), 2014
Balog A; Rivat J; Sárközy A: On arithmetic properties of sumsets, Acta Math. Hungar. (közlésre elfogadva), 2014
Gyarmati K; Sárközy A: On reducible and primitive subsets of F_p, Integers (EJCNT), 2014
Mérai L: On the elliptic curve power generator, Uniform Distribution Theory, 2014
Bárász M; Ligeti P; Lónya K; Mérai L; Nagy D. A.: An another twist in the Dining Cryptographers' protocol, Tatra Mt. Math. Publ., 2014
Farkas B; Pintz J; Révész Sz. Gy: On the weight function in GPY for small gaps between primes, Number Theory, Combinatorics and Analysis, W. de Gruyter, 75-104, 2013
Goldston D. A; Graham S. W; Pintz J; Yildirim C. Y: Corrigendum: Small gaps between products of two primes, Proc. Lond. Math. Soc. (3) 106: 477-480, 2013
Pintz J: Paul Erdős and the difference of primes, Bolyai Soc. Math. Studies 25, Erdős centennial, eds. L. Lovász et al., Springer, 485-513, 2013
Pintz J: Some new results on small gaps between consecutive primes, Number Theory, Analysis and Combinatorics, W. de Gruyter, Berlin, 231-247, 2013
Pintz J: The twin prime conjecture, bounded gaps between consecutive primes, and Polignac numbers, Eureca, The Archimdians Journal, 2014
Károlyi Gy: Proof of a conjecture of Farhi, Asian-European Journal of Mathematics (közlésre elfogadva), 2014
Károlyi Gy; Nagy Z. L; Petrov F. V; Volkov V: A new approach to constant term identities and Selberg-type integrals, Advances in Mathematics (közlésre benyujtva), 2014
Gyarmati K; Mauduit C; Sárközy A: On linear complexity of binary lattices, II, Ramanujan J. 34(2): 237-263, 2014
Mérai L: The higher dimensional analogue of certain estimates of Roth and Sárközy, Periodica Math. Hungar. 68: 77-91, 2014
Schneider P; Vigneras MF; Zábrádi G: From étale P_+ representations to G equivariant sheaves on G/P, Automorphic Forms and Galois Representations, London Math. Soc. Lecture Notes Series 415, eds. F Diamond et al., Vol. 2, 248-366, 2014
Zábrádi G: (phi,gamma)-modules over noncommutative overconvergent and Robba rings, Algebra and Number Theory 8(1): 191-242, 2014
Gyarmati K; Mauduit C; Sárközy A: The cross-correlation measure for families of binary sequences, Applied Algebra and Number Theory, Essays in Honor of Harald Niederreiter on the occasion of his 70th birthday, eds. G. Larcher et al., Cambridge Univ. Press, 126-143, 2014
Gyarmati K; Sárközy A: On reducible and primitive subsets of F_p, Integers (EJCNT) (közlésre benyujtva), 2014
Mérai L: On the elliptic curve power generator, Uniform Distribution Theory 9(2): 59-65, 2014
Pintz J: The twin prime conjecture, bounded gaps between consecutive primes, and Polignac numbers, Eureca, The Archimedians Journal (közlésre benyujtva), 2014
Károlyi Gy: Proof of a conjecture of Farhi, Asian-European Journal of Mathematics 7: 145002 (5 pages), 2014
Bíró A.: An identity related to Wilson functions, Acta Math. Hungar. 144(2): 367-406, 2014
Gyarmati K.: On the complexity of a family based on irreducible polynomials, Finite Fields and Their Applications (közlésre elfogadva), 2014
Hegyvári N., Hennecart F: On the distribution of the values of multivariate rational functions, Uniform Distribution Theory (közlésre elfogadva), 2014
Hegyvári N., Hennecart F.: Note on a result of Chung on Weil type sums, Integers (EJCNT) (közlésre benyujtva), 2014
Mérai L.: On the typical values of the cross-correlation measure, Monatshefte Math. (közlésre benyujtva), 2014
Mérai L.: Pseudorandomness of binary sequences derived from linear recursions, Periodica Math. Hungar. (közlésre elfogadva), 2014
Mérai L., Yayla O.: Improving results on the pseudorandomness of sequences generated via the additive order, Discrete Math. (közlésre benyujtva), 2014
Pintz J.: New equidistribution estimates of Zhang type, and bounded gaps between primes, D. H. J. Polymath, Algebra and Nunber Theory (közlésre elfogadva), 107 oldal, 2014
Pintz J.: On the ratio of consecutive gaps between primes, arXiv:1406.2658v2 (24 oldal), 2014
Pintz J.: On the distribution of gaps between consecutive primes, arXiv:1407.2213v2 (22 oldal), 2014
Rivat J., A. Sárközy: On arithmetic properties of products and shifted products, Analytic Number Theory, In Honor of Helmut Maier's 60th Birthday, Springer (közlésre elfogadva), 2014
Gyarmati K., Mauduit C., Sárközy A: Generation of further pseudorandom binary sequences, I (Blowing up a single sequence), Uniform Distribution Theory (közlésre elfogadva), 2014
Sárközy A.: On pseudorandomness of families of binary sequences, J. Applied Discrete Math. (közlésre benyujtva), 2014
Gyarmati K., Mauduit C., Sárközy A.: On finite pseudorandom binary lattices, J. Applied Discrete Math. (közlésre benyujtva), 2014
Sebők R.: On a connection berween pseudorandom measures, Uniform Distribution Theory (közlésre benyujtva), 2014
Sebők R.: On pseudorandom binary sequences constructed by using finite fields, Periodica Math. Hungar. (közlésre benyujtva), 2014
Backhausz T., Zábrádi G.: Algebraic functional equations and completely faithful Selmer groups, International J. Number Theory (közlésre benyujtva), 2014
Erdélyi M., Zábrádi G.: Links between generalized Montréal functors, http://www.cs.elte.hu/~zger/SVtoB.pdf, 2014
Goldston D. A., Pintz J., Yildirim C. Y.: Small gaps between primes, ICM Proceedings, Soeul, 2014
Dartyge C; Mauduit C; Sárközy A: Polynomial values and generators with missing digits in finite fields, Funct. Approx. Comment. Math. 52(1): 65-74, 2015
Károlyi Gy; Lascoux A; Warnaar SO: Constant term identities and PoincarÉ polynomials, Trans. Amer. Math. Soc. 367: 6809-6836, 2015
Károlyi Gy.: A Lie algebra approach to difference sets: Homage to Yahia Ould Hamidoune, Annales Univ. Sci. Budapest. Eötvös, Sectio Math. 57: 77-83, 2014
Balog A; Rivat J; Sárközy A: On arithmetic properties of sumsets, Acta Math. Hungar. 144(1): 18-42, 2014
Gyarmati K; Sárközy A: On reducible and primitive subsets of F_p, Integers (EJCNT) 15A: No. A6, 21 pp, 2015
Bárász M; Ligeti P; Lónya K; Mérai L; Nagy D. A.: An another twist in the Dining Cryptographers' protocol, Tatra Mt. Math. Publ. 57: 85-99, 2013
Károlyi Gy; Nagy Z. L; Petrov F. V; Volkov V: A new approach to constant term identities and Selberg-type integrals, Advances in Mathematics 277: 252-282, 2015
Gyarmati K.: On the complexity of a family of Legendre sequences with irreducible polynomials, Finite Fields and Their Applications 33: 175-186, 2015
Hegyvári N., Hennecart F.: Note on a result of Chung on Weil type sums, Integers (EJCNT) 15, No. A37, 9 pp, 2015
Mérai L.: Pseudorandomness of binary sequences derived from linear recursions, Periodica Math. Hungar. 71: 64-77, 2015
Mérai L., Yayla O.: Improving results on the pseudorandomness of sequences generated via the additive order, Discrete Math. 338: 2020-2025, 2015
Pintz J.: New equidistribution estimates of Zhang type, and bounded gaps between primes, D. H. J. Polymath, Algebra and Nunber Theory: 2067-2199, 2014
Pintz J.: On the ratio of consecutive gaps between primes, Analytic Number Theory, In Honor of Helmut Maier's 60th Birthday, eds. C. Pomerance et al., Springer: 285-304, 2015
Rivat J., A. Sárközy: On arithmetic properties of products and shifted products, Analytic Number Theory, In Honor of Helmut Maier's 60th Birthday, eds. C. Pomerance et al., Springer, 343-355, 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
Sebők R.: On a connection berween pseudorandom measures, Uniform Distribution Theory 10: 107-113, 2015
Sebők R.: On pseudorandom binary sequences constructed by using finite fields, Periodica Math. Hungar. 71: 210-223, 2015
Backhausz T., Zábrádi G.: Algebraic functional equations and completely faithful Selmer groups, International J. Number Theory 11(4): 1233-1257, 2015
Károlyi Gy, Komjáth P: Well ordering groups with no monotone arithmetic progressions, Order (közlésre benyujtva), 2015
Dartyge C.; Szalay M.: On a phenomenon of Turán concerning the summands of partitiona, Acta Math. Hungar. (közlésre benyujtva), 2015
Mérai L.: The cross-correlation measure of families of finite binary sequences: limiting distributions and minimal values, Discrete Applied Math. (közlésre elfogadva), 2015
Mérai L.; Winterhof A.: On the linear complexity profile of some sequences derived from elliptic curves, Des. Codes Cryptogr. (közlésre elfogadva), 2015
Mérai L.; Winterhof A.: On the pseudorandomness of the Liouville function of polynomials over a finite field, Unif. Distr. Theory (közlésre elfogadva), 2015
Dartyge C.; Gyarmati K.; Sárközy A.: On irregularities of distribution of binary sequences relative to arithmetic progressions, I. (General results), Unif. Distrib. Theory (közlésre elfogadva), 2015
Gyarmati K.; Sárközy A.: On reducible and primitive subsets of F_p, II, Quart. J. Math. Oxford, Quart. J. Math. Oxford (közlésre elfogadva), 2015
Mauduit C.; Rivat J.; Sárközy A.: On the digits of sumsets, Canadian J. Math. (közlésre banyujtva), 2015
Pintz J.: Polignac Numbers, Conjectures of Erdős on Gaps Between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture, From Arithmetic to Zeta Functions - Number Theory on Memory of Wolfgang Schwarz, eds. J. Sander et al., Springer (közlésre benyujtva), 2015
Pintz J.: An approximation to the twin prime conjecture and the parity phenomenon, Indag. Math. 26: 883-896, 2015
Zábrádi G.: Multivariate (phi,gamma)-modules and smooth o-torsion representations, J. European Math. Soc. (közlésre benyujtva), 2015
Chen Y.-G.; Fang J.-H.; Hegyvári N.: On the subset sums of exponential type sequences, Acta Arith. (közlésre elfogadva), 2015
Chen Y.-G.; Fang J.-H.; Hegyvári N.: Erdős-Birch type question in N^r, Monatshefte Math. (közlésre benyujtva), 2015
Hegyvári N.; Hennecart F.: Expansion for cubes in the Heisenberg group, Forum Mathematicum (közlésre benyujtva), 2015
Hegyvári N.: On deterministic and random rolling of polyhedra, Int.Electron. J. Geom. (közlésre benyujtva), 2015
Bíró A.; Lapkova K.: The class number one problem for the real quadratic fields Q[(an^2+4a)^1/2], Acta Arith. (közlésre elfogadva), 2015
Jha S.; Ochiai T.; Zábrádi G.: On twists of modules over non-commutative Iwasawa algebras, Algebra and Number Theory (közlésre benyujtva), 2015




 

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2016-03-31 09:53:50
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