Additive problems and Fourier analysis  Page description

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Details of project

 
Identifier
81658
Type K
Principal investigator Ruzsa, Imre
Title in Hungarian Additiv problemak es Fourier analizis
Title in English Additive problems and Fourier analysis
Keywords in Hungarian Additiv problemak, Fourier analizis, additiv szamelmelet
Keywords in English Additive problems, Fourier analysis, additive 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, HAS
Participants Balog, Antal
Biró, András
Böröczky, Károly
Hegyvári, Norbert
Krenedits, Sándor
Matolcsi, Máté
Révész, Szilárd
Sándor, Csaba
Starting date 2010-02-01
Closing date 2013-12-31
Funding (in million HUF) 9.849
FTE (full time equivalent) 15.97
state closed project
Summary in Hungarian
Az additiv számelmélet és valós analízis látszólag távoli témák, mégis szorosan kapcsolódnak.
Nem csak a számelmélet használja az analízist a generátorfüggvény elven keresztül, hanem
a Fourier analizis is gyakran használ számelméleti vagy kombinatorikus konstrukciókat.
Ráadásul számelméleti alkalmazások is gyakran inspirálják tisztán analitikus tételek kifejlesztését.
A kutatás tipikus módszerei a trigonometrikus összegek és karakter összegek becslései, illetve általában a Fourier analízis eszközei. Az említett két terület közötti összetett kölcsönhatás motiválja kutatásainkat.
Summary
There is a close connection between the apparently different disciplines, additive number theory and real analysis. Not only number theory uses much analysis by the generating function principle, but also Fourier analysis uses much number theoretical and combinatorial constructions. In addition, number theoretical applications inspire development of pure analytic tools and theorems. Trigonometric sums, character sums and Fourier analysis provide the typical tools to attack our problems. The complex interaction between the two fields motivates the planned research.





 

Final report

 
Results in Hungarian
A projekt során a kutatási tervnek megfelelően elsősorban additív számelméleti és additív kombinatorikai problémakörökben értünk el új eredményeket. A bizonyítási módszerekben központi szerep jutott a Fourier analitikus módszereknek, de természetesen ezen felül megjelentek a számelmélet, a kombinatorika és az analízis klasszikus és modern módszerei is. A projekt keretében 44 tudományos publikáció született. A konkrét eredmények igen szerteágazóak, és részletes leírást a csatolt beszámoló tartalmaz.
Results in English
In accordance with the original research plan we have made scientific contributions mainly to problems in additive number theory and additive combinatorics. The used methods were centered around the use of Fourier analysis, but other calssical and modern tools of number theory, combinatorics and analysis were also applied. In the span of the project we have published 44 scientific papers. The actual results are rather wide-spread and we have included a detailed description of them in the attached file.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=81658
Decision
Yes





 

List of publications

 
N. Hegyvári, F. Hennecart: Conditional expanding bounds for two-variable functions over prime fields, European Journal of Combinatorics 34 (2013) 1365–1382, 2013
N. Hegyvári, F. Hennecart: A structure result for bricks in Heisenberg groups, Journal of Number Theory 133 (2013) pg. 2999–3006., 2013
N. Hegyvári, F. Hennecart: Substructure for product set in the Heisenberg groups, Moscow J. of Comb. and Numb. Th. 2013, vol.3. iss. 1. pp. 57-68, 2013
M. Matolcsi: A Fourier analytic approach to the problem of mutually unbiased bases, Studia Sci. Math. Hung., Vol. 49, No. 4 (2012), 482-491., 2012
M. Matolcsi, I. Z. Ruzsa: Sets with no solutions to x+y=3z, European J. Combin., 34 (2013), no. 8, 1411–1414., 2013
M. Matolcsi, I. Z. Ruzsa, M. Weiner: Real and complex unbiased Hadamard matrices, Australasian J. Combinatorics, Volume 55 (2013), Pages 35–47., 2013
R. D. Malikiosis, M. Matolcsi, I. Z. Ruzsa: A note on the pyjama problem, Eur. J. Comb, Volume 34, Issue 7, October 2013, Pages 1071–1077., 2013
M. Matolcsi, I. Z. Ruzsa: Difference sets and positive exponential sums I. General properties., Journal of Fourier Anal. Appl., DOI: 10.1007/s00041-013-9299-9 published online 19. Nov. 2013., 2013
Csaba Sándor, Eszter Rozgonyi: A Converse to an Extension of a Theorem of Erdős and Fuchs, Journal of Combinatorics and Number Theory, megjelenés alatt, 2014
Csaba Sándor, Sándor Z. Kiss, Eszter Rozgonyi: Sets with almost coinciding representation functions, Bulletin of the Australian Mathematical Society, megjelenés alatt, 2014
Sándor Z. Kiss, Eszter Rozgonyi, Csaba Sándor: On additive complement of a finite set, Journal of Number Theory 136C (2014), pp. 195-203, 2014
Bálint Farkas, János Pintz and Szilárd Gy. Révész: On the optimal weight function in the Goldston-Pintz-Yildirim method for finding small gaps between consecutive primes, Paul Turán Memorial Volume: Number Theory, Analysis and Combinatorics, de Gruyter, Berlin, 23 pages, megjelenés alatt., 2014
Sz. Gy. Révész: Turán-Erőd Type Converse Markov Inequalities for Convex Domains on the Plane, Proc. of Int. Conference "Complex Function Theory and Applications '13", V. Kiryakova (Ed.), 2013 (electr.), Inst. of Math. and Inf., Bulg. Acad. Sci. Sofia, 252-281, 2013
K.J. Boroczky, E. Lutwak, D. Yang, G. Zhang: AFFINE IMAGES OF ISOTROPIC MEASURES, J. Diff. Geom., megjelenés alatt, 2014
A. Biró: Some Properties of Wilson Functions, Acta Math. Hungar., 137 (3) (2012), 158-190, 2012
SZILÁRD GY. RÉVÉSZ: Turán´s extremal problem on locally compact abelian groups, Analysis Mathematica, 37 (2011), 15-50, 2011
A. Balog, K.A. Broughan, I.E.Shparlinski: On the number of solutions of exponential congruences, Acta Arithmetica, 148 (2011), 93-103., 2011
A. Biró: A relation between triple products of weight 0 and weight 1/2 cusp forms, Israel J. Math. 182 (2011), 61–101, 2011
N. Hegyvári: Symmetry sets, Approximate groups, J. of Combinatorics and Number Theory, JCNT, 2011, Volume 1. Number 3. pp. 1-6, 2011
N. Hegyvári, F. Hennecart: Distribution of residues in approximate subgroups of F_p^*, Proc. Amer Math. Soc., Volume 140, Number 1, January 2012, Pages 1–6, 2012
M. Matolcsi, C. Vinuesa: Improved bounds on the supremum of autoconvolutions, Journal of Mathematical Analysis and Applications, Vol. 372, Issue 2, (2010), 439-447., 2010
M. N. Kolountzakis, M. Matolcsi: Teselaciones por traslación, La Gaceta de la Real Sociedad Matematica Espanola, Vol. 13 (2010), Num. 4, 725–746., 2010
Katalin Gyarmati, M.Matolcsi, and I.Z. Ruzsa: A superadditivity and submultiplicativity property for cardinalities of sumsets., Combinatorica, 30:163--174, 2010., 2010
M.Matolcsi and I.Z. Ruzsa.: Sumsets and the conves hull, Additive Number Theory: in honor of the sixtieth birthday of M. B. Nathanson, pages 221--228. Springer, 2010., 2010
I.Z. Ruzsa: Towards a noncommutative Plünnecke-type inequality, An irregular mind Szemerédi is 70, volume~21 of Bolyai Society Mathematical Studies, pages 591--605, 2010., 2010
J.Cilleruelo, S.Z. Kiss, I.Z. Ruzsa, and C.Vinuesa: Generalization of a theorem of Erdős and Rényi on Sidon sequences, Random Structures and Algorithms, 37:455--464, 2010., 2010
J.Cilleruelo, I.Z. Ruzsa, and C.Vinuesa: Generalized Sidon sets, Advances in Math., 255:2786--2807, 2010., 2010
R.Crowston, G.Gutin, M.Jones, E.J. Kim, and I.Z. Ruzsa: Systems of Linear Equations over F_2 and Problems Parameterized Above Average, 12th Scandinavian Symposium and Workshops on Algorithm Theory, pages 164--175, 2010., 2010
Stephan Brandt, Jozef Miskuf, Dieter Rautenbach, Friedrich Regen, and Imre Z. Ruzsa.: Edge-injective and edge-surjective vertex labellings, SIAM J. Discrete Math., 24(2):666--683, 2010., 2010
I.Z. Ruzsa and P.Varjú: Euclidean algorithm in different norms., Publ. Math. Debrecen, 78:245--249, 2011., 2011
A. Biró: An expansion theorem concerning Wilson functions and polynomials, Acta Mathematica Hungarica, 135 (4) (2012), 350-382, 2012
S. Krenedits: Three-term idempotent counterexamples in the Hardy-Littlewood majorant problem, J. Math. Anal. Appl. 388 (2012) 136-150., 2012
N. Hegyvári: Some Remarks on Multilinear Exponential Sums with an Application, Journal of Number Theory, Volume 132, Issue 1, January 2012, Pages 94-102., 2012
N. Hegyvári, F. Hennecart: A Note on Freiman models in Heisenberg groups, Israel Journal of Mathematics, June 2012, Volume 189, Issue 1, pp 397-411., 2012
A. Balog, A. Cojacaru, C. David:: Average twin prime conjecture for elliptic curves, Amer. Journal of Math. 133 (2011), 1179-1229., 2011
A. Balog: A note on sum-product estimates, Publ. Math. Debrecen, 79/3 4 (2011), 283-289., 2011
A. Balog, C. Dartyge: On the sum of digits of multiples, Moscow J. of Combinatorics and Number Theory, 2/1 (2012), 3-15., 2012
A. Balog, K. A. Broughan, Igor E. Shparlinski:: Sum-product estimates with several sets and applications, Integers J, Vol. 12, (2012), 895-906., 2012
Gyarmati, Katalin; Ruzsa, Imre Z.: A set of squares without arithmetic progressions, Acta Arith. 155, No. 1, 109-115 (2012)., 2012
A. Biró: A duality relation for certain triple products of automorphic forms, Israel Journal of Mathematics, 192 (2) (2012), 587-636,, 2012
Antal Balog: Another sum-product estimate in finite fields, Sovrem. Probl. Mat., Steklov Math. Inst. RAS, 16 (2012), 31-37., 2012
Anne de Roton, Szilárd Gy. Révész: Generalization of the effective Wiener-Ikehara theorem, Int. J. Number Theory Vol. 9, No. 8 (2013) 2091-2128., 2013
Krenedits, Sándor: On Mockenhoupt's Conjecture in the Hardy-Littlewood Majorant Problem, Journal of Contemporary Mathematical Analysis (Izv. Arm. Acad. Nauk) 48 (2013), no. 3., 91--109., 2013
Krenedits, Sándor: Special quadrature error estimates and their application in the Hardy-Littlewood majorant problem, Acta Mathematica Academiae Paedagogicae Nyregyhaziensis 28 (2012), 121-151, 2012





 

Events of the project

 
2013-10-16 18:07:21
Résztvevők változása
2011-08-29 10:35:13
Résztvevők változása




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