Additive Problems and Fourier Analysis  Page description

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Details of project

 
Identifier
109789
Type K
Principal investigator Ruzsa, Imre
Title in Hungarian Összeghalmazok és Fourier Analízis
Title in English Additive Problems and Fourier Analysis
Keywords in Hungarian Additiv problemak, Fourier analizis, additiv szamelmelet
Keywords in English Additive number theory, Fourier analysis; additive problems
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
Kiss, Sándor
Matolcsi, Máté
Révész, Szilárd
Sándor, Csaba
Starting date 2014-01-01
Closing date 2018-12-31
Funding (in million HUF) 20.092
FTE (full time equivalent) 10.18
state running project





 

Final report

 
Results in Hungarian
A projekt során a kutatási tervnek megfelelően számos eredményt értünk el olyan kérdésekkel kapcsolatban, ahol bizonyos halmazok additív struktúráját illetve számosságát vizsgáltuk a Fourier analízis eszközeivel és egyéb módszerekkel. A résztvevők között több eredményes együttműködés is létrejött, amelynek eredményeképp a kutatási tervben megjelölt minden fő területen sikerült előrelépést elérni. Ezek a témakörök a következők: Sidon halmazok és additív reprezentációs függvények tulajdonságai, differencia halmazok és karakterösszegek kapcsolata, Erdős-féle kérdések a diszkrét geometria és additiív kombinatorika kapcsolatáról (összeg-szozat típusú problémák), expanderek kommutatív és nem-kommutatív csoportokban, és a diszkrét Brunn-Minkowski egyenlőtlenség. Ezeken felül természetesen egyéb kapcsolódó témakörökkel is foglalkoztunk és értünk el eredményeket, ahogy az a matematikai kutatás során adódni szokott. A konkrét eredmények összefoglalóját a feltöltött beszámolóban adtuk meg.
Results in English
During the project we have achieved several results concerning additive structures and cardinalities of certain sets with the use of Fourier analysis and other mathematical tools. Several fruitful collaborations have been formed among the researchers and, as a result, we have made progress in all major areas described in the project plan. These areas are as follows: properties of Sidon sets and additive representation functions, the relation of difference sets and character sums, Erdos-type problems relating discrete geometry and additive combinatorics (sum-product phenomena), expanders in Abelian and non-Abelian groups, and the discrete version of the Brunn-Minkowski inequality. Besides these results have made progress in other related questions as well, as it typically happens in mathematical research. The description of the specific results is given separately in an uploaded file.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=109789
Decision
Yes





 

List of publications

 
K.J. Boroczky, F. Fodor, D. Hug: Strengthened volume inequalities for $L_p$ zonoids of even isotropic measures, Trans. AMS, 371, 505-548., 2019
K.J. Boroczky, M. Ludwig: Minkowski valuations on lattice polytopes, JEMS, 21, 163-197., 2019
K.J. Boroczky, A. Kovacs: The isoperimetric problem for 3-polytopes with six vertices, Annales Universitatis Scientiarium Budapestinensis de Rolando Eotvos Nominatae Sectio Mathematica, 61, 55-67., 2018
K. J. Böröczky, M. Matolcsi, I. Z. Ruzsa, F. Santos, O. Serra: Triangulations and a discrete Brunn-Minkowski inequality in the plane, submitted for publication, 2019
M. Kolountzakis, M. Matolcsi, M. Weiner: An application of positive definite functions to the problem of MUBs, Proc. AMS, Volume 146, Number 3, 1143-1150, 2018
M. Matolcsi, M. Weiner: Finite projective planes and the Delsarte LP-bound, Analysis Math., 44 (1), 89–98, 2018
M. Matolcsi, M. Weiner: Character tables and the problem of existence of finite projective planes, Journal of Combinatorial Designs, Vol. 26, Issue 11, 540-546., 2018
Imre Z. Ruzsa, Dmitrii Zhelezov: Convex sequences may have thin additive bases, Moscow J. Comb. Number Theory, Vol 8, 43-46, 2019
Gautami Bhowmik, Imre Z. Ruzsa: Average Goldbach and the Quasi-Riemann Hypothesis, Analysis Mathematica, Volume 44, Issue 1, pp 51–56, 2018
Ben Green, Imre Z. Ruzsa: On the arithmetic Kakeya conjecture of Katz and Tao, Periodica Math. Hung., to appear, 2019
Oliver Roche-Newton, Imre Z. Ruzsa, Chun-Yen Shen, Ilya D. Shkredov: On the size of the set AA+A, submitted for publication, 2019
S. Z. Kiss, Cs. Sándor, Q-H Yang: On generalized Stanley sequences, Acta Mat. Hungar. 154, no 2, 501–510., 2018
Cs. Sándor, Q-H Yang: On some properties of representation functions related to the Erdõs-Turán conjecture, European J. Combin. 71, 222–228., 2018
S. Z. Kiss, Cs. Sándor, Q-H Yang: On a conjecture of Erdõs about sets without k pairwise coprime integers, SIAM J. Discrete Math. 32 no. 4, 2453–2466., 2018
P. P. Pach, Cs. Sándor: Multiplicative Bases and an Erdõs Problem, Combinatorica 38, no. 5, 1175–1203., 2018
S. Z. Kiss, Cs. Sándor, Q-H Yang: On minimal additive complements of integers, J. Combin. Theory Ser. A 162, 344–353., 2019
P. P. Pach, Cs. Sándor: On infinite multiplicative Sidon sets, European J. Combin. 76, 37–52., 2019
S. Kiss, Cs.Sandor: Generalization of some results about the regularity properties of an additive representation function, Acta Mathematica Hungarica, to appear, 2019
A. Biro: Local average of the hyperbolic circle problem for Fuchsian groups, Mathematika 64, 159–183, 2018
A Biro, V.F. Lev: Uncertainty in finite planes, submitted for publication, 2019
Cs. Csapodi , N. Hegyvari: On some irrational decimal fractions, revisited, ELEMENTE DER MATHEMATIK 73:(1) pp. 23-28., 2018
N. Hegyvari, F. Hennecart: Expansion for cubes in the Heisenberg group, FORUM MATHEMATICUM 30:(1) pp. 227-236., 2018
N. Hegyvári, F. Hennecart: A note on the size of the set A^2+A, RAMANUJAN JOURNAL, Vol. 46, Issue 2, pp 357-372, 2019
P. Yu. Glazyrina, Sz. Gy. Révész,: Turán-Erőd type converse Markov inequalities on general convex domains of the plane in L^q, Proceedings of the Steklov Institute of Mathematics, to appear, 2019
B. Farkas, B. Nagy, Sz. Gy. Révész: A potential theoretic minimax problem on the torus, Trans. London Math. Soc. 5, no. 1, 1–46., 2018
S. Krenedits, Sz. Gy. Révész: The point value maximization problem for positive definite functions supported in a given subset of a locally compact group, Proc. Edinb. Math. Soc. (2) 61, no. 1, 179–200., 2018
Marton Horvath, Imre Z Ruzsa: Connections between the cardinality of sumsets and difference sets near the extreme, Ann. Univ. Sci. Budapest, 59, 137-142., 2016
João Guerreiro, Imre Z. Ruzsa, Manuel Silva: Monochromatic paths for the integers, European Journal of Combinatorics 58, pp. 283-288, 2016
Andras Biro: Some integrals of hypergeometric functions, Acta Math. Hungar. 152, no. 1, 58–71., 2017
Antal Balog, Oliver Roche-Newton, Dmitry Zhelezov: Expanders with superquadratic growth, Electron. J. Combin. 24, no. 3, Paper 3.14, 17 pp., 2017
Antal Balog, Trevor D. Wooley: A low-energy decomposition theorem, Q. J. Math. 68, no. 1, 207–226., 2017
Antal Balog, Andrew Granville, Jozsef Solymosi: Gaps between fractional parts, and additive combinatorics, Q. J. Math. 68, no. 1, 1–11., 2017
Polina Yu Glazyrina, Szilárd Gy. Révész: Turán type converse Markov inequalities in Lq on a generalized Erőd class of convex domains, J. Approx. Theory 221, 62–76., 2017
Andrey Efimov, Marcell Gaál, Szilárd Gy. Révész: On integral estimates of nonnegative positive definite functions, Bull. Aust. Math. Soc. 96, no. 1, 117–125., 2017
Polina Yu Glazyrina, Szilárd Gy. Révész: Turán type oscillation inequalities in Lq norm on the boundary of convex domains, Math. Inequal. Appl. 20, no. 1, 149–180., 2017
Sándor Z. Kiss, Csaba Sándor: On the multiplicativity of the linear combination of additive representation functions, Ramanujan J. 44, no. 2, 385–399., 2017
Sándor Z. Kiss, Csaba Sándor: Partitions of the set of nonnegative integers with the same representation functions, Discrete Math. 340, no. 6, 1154–1161., 2017
Csaba Sándor, Quan-Hui Yang: A lower bound of Ruzsa's number related to the Erdős-Turán conjecture, Acta Arith. 180, no. 2, 161–169., 2017
Eszter Rozgonyi, Csaba Sándor: An extension of Nathanson's theorem on representation functions, Combinatorica 37, no. 3, 521–537., 2017
Károly J. Böröczky, Monika Ludwig: Valuations on lattice polytopes, Tensor valuations and their applications in stochastic geometry and imaging, 213–234, Lecture Notes in Math., 2177, Springer, Cham, 2017
Károly J. Böröczky, Daniel Hug: Isotropic measures and stronger forms of the reverse isoperimetric inequality, Trans. Amer. Math. Soc. 369, no. 10, 6987–7019., 2017
Károly J. Böröczky, Hai T. Trinh: The planar Lp-Minkowski problem for 0, Adv. in Appl. Math. 87, 58–81., 2017
Károly J. Böröczky, Martin Henk: Cone-volume measure and stability, Adv. Math. 306, 24–50., 2017
A. Balog, O. Rochet-Newton: New sum-product estimates for real and complex numbers, Discrete and Computational Geometry, Vol. 53, 825-846., 2015
A. Balog, G. Shakan: Sum of dilates in vector spaces,, North-Western European Journal of Mathematics, Vol. 1, 46--54, 2015
Károly J. Böröczky, Hai T. Trinh: The planar L_p-Minkowski problem for 0 < p < 1., Adv. in Appl. Math. 87, 58–81., 2017
K.J. Boroczky, Francesco Santos, Oriol Serra: On sumsets and convex hull, Disc. Comp. Geom., 52, 705-729., 2014
G. Ambrus, K.J. Boroczky: Stability results for the volume of random simplices, American Journal of Math., 136, 833-857, 2014
F. Barthe, K.J. Boroczky, M. Fradelizi: Stability of the functional version the Blaschke-Santalo inequality, Monatshefte Math., 173, 135-159, 2014
A. Balog, J. Rivat, A. Sarkozy: On arithmetic properties of sumsets, Acta Math. Hungar. 144, 18–42., 2014
A. Balog, G. Shakan: On the sum of dilations of a set, Acta Arith. 164, 153–162., 2014
N. Hegyvári, F. Hennecart: On the distribution of the values of multivariate rational functions, Uniform Distribution Theory 9, 103–123, 2014
M. Matolcsi, I.Z. Ruzsa: Difference sets and positive exponential sums I. General properties, J. Fourier Anal. Appl. 20, 17–41., 2014
A. Biro: An identity related to Wilson functions, Acta Mathematica Hungarica, 144, 367-406, 2014
B. Farkas, Sz. Gy. Revesz: The periodic decomposition problem, in: Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer Proceedings in Mathematics & Statistics 102 (Proceedings of the Int. Conf. on, 2014
A.Z. Kiss, E. Rozgonyi, Cs. Sandor: On Sidon sets which are asymptotic bases of order 4, Funct. Approx. Comment. Math. 51, 393–413., 2014
A.Z. Kiss, E. Rozgonyi, Cs. Sandor: Sets with almost coinciding representation functions, Bull. Aust. Math. Soc. 89, 97–111., 2014
A.Z. Kiss, E. Rozgonyi, Cs. Sandor: On additive complement of a finite set, J. Number Theory 136, 195–203., 2014
N. Hegyvári, F. Hennecart: Note on a a result of Chung on Weil type sums, Integers, Vol. 15, Paper A37,, 2015
N. Hegyvári: Note on character sums of Hilbert cubes, J. of Number Theory, Volume 160, Pages 526-535, 2015
A. Balog, O. Rochet-Newton: New sum-product estimates for real and complex numbers, Discrete and Computational Geometry, Vol. 53, 825-846., 2015
A. Balog, G. Shakan: Sum of dilates in vector spaces,, North-Western European Journal of Mathematics, Vol. 1, 46--54, 2015
K.J. Böröczky, E. Lutwak, D. Yang, G. Zhang: Affine images of isotropic measures, J. Diff. Geom., Vol. 99, 407-442., 2015
K.J. Böröczky, P. Hegedűs: The cone volume measure of antipodal points, Acta Mathematica Hungarica, Vol. 146, 449-465, 2015
K.J. Böröczky, B. Hoffman: A note on triangulations of sum sets, Involve - a Journal of Mathematics, 8, 75-85., 2015
S. Krenedits, Sz. Gy. Révész: Carathéodory-Fejér type exremal problems on locally compact groups, J. Approx Theory Vol. 194, 108-131, 2015
S. Z. Kiss, E. Rozgonyi, Cs. Sándor: Groups, partitions and representation functions, Publ. Math. Debrecen, Vol 85, no. 3-4, 425–433., 2014
P. Jaming, M. Matolcsi: On the existence of flat orthogonal matrices, Acta Math. Hung., Vol. 147, Issue 1, 179-188., 2015
M. Matolcsi, M. Weiner: An Improvement on the Delsarte-Type LP-Bound with Application to MUBs, Open Systems & Information Dynamics, Vol. 22, No. 1, 2015
M. Matolcsi: A Walsh-Fourier approach to the circulant Hadamard conjecture, In: Algebraic Design Theory and Hadamard Matrices; C. J. Colbourn (ed), Springer Proceedings in Mathematics and Statistics 133 (2015), 201-208., 2015
N. Hegyvári: Note on character sums of Hilbert cubes, J. of Number Theory, Volume 160, Pages 526-535, 2016
I.Z. Ruzsa: Exact additive complements, Quart. J. Math. Oxford, :1–9, 2016. doi:10.1093/qmath/haw029, 2016
A. Biró, K. Lapkova: The class number one problem for the real quadratic fields $\mathbb{Q}\left(\sqrt{(an)^2+4a}\right)$, Acta Arithmetica, 2016, 172(2): 117-131, 2016
Szilárd Gy. Révész: A discrete extension of the Blaschke rolling ball theorem, Geom Dedicata, 182 (2016), 51–72., 2016
T. Keleti, M. Matolcsi, F. M. Oliveira Filho, I. Z. Ruzsa: Better bounds for planar sets avoiding unit distances, Disc. Computational Geometry, 55(3), 642-661., 2016
S.Z. Kiss, Cs. Sándor: On the maximum values of the additive representation functions, Int. J. Number Theory 12 (2016), no. 4, 1055–1075., 2016
A. Balog, T. Wooley: A low-energy decomposition theorem, Quart. J. of Math., Oxford (2016), doi:10.1093/qjmath/haw023, 2016
A. Balog, A. Granville, J. Solymosi: Gaps between fractional parts and additive combinatorics, Quart. J. of Math., Oxford (2015), doi:10.1093/qmath/hav012, 2016
Y G Chen, J-H Fang, N Hegyvári: On the subset sums of exponential type sequences, ACTA ARITHMETICA 173:(2) pp. 141-150., 2016
N Hegyvári: On Deterministic and Random Rolling of Polyhedra, INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY 9:(1) pp. 85-88., 2016
N. Hegyvari, I.Z. Ruzsa: Additive structure of difference sets and a theorem of Folner, Australian Journal of Combinatorics 64: pp. 437-443., 2016
K.J. Böröczky, M. Henk: Cone-volume measure of general centered convex bodies., Advances Math., 286 (2016), 703-721., 2016
K.J. Böröczky, P. Hegedűs, G. Zhu: On the discrete logarithmic Minkowski problem, IMRN, Int. Math. Res. Not., 6 (2016), 1807-1838., 2016
K.J. Böröczky: Translation invariant Minkowski valuations on lattice polytopes, In: F. Barthe, M. Henk, M. Ludwig (eds), Oberwolfach Report No. 56/2015, (2016), 3193-3195., 2016
Francesco Monopoli, Imre Z. Ruzsa: Carries and the arithmetic progression structure of sets., Integers 17, Paper No. A8, 21 pp., 2017
Imre Z Ruzsa: Exact additive complements., Q. J. Math. 68, no. 1, 227–235., 2017





 

Events of the project

 
2017-05-02 10:48:27
Résztvevők változása




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