An elementary analog of the operator method in additive combinatorics. (English. Russian original) Zbl 1468.11035
Math. Notes 109, No. 1, 110-119 (2021); translation from Mat. Zametki 109, No. 1, 117-128 (2021).
Summary: This paper provides an elementary proof of inequalities previously obtained by the operator method and having applications in additive combinatorics. The method of proof allows us to take a new look at a certain special case of Sidorenko’s conjecture.
MSC:
| 11B13 | Additive bases, including sumsets |
| 11B30 | Arithmetic combinatorics; higher degree uniformity |
| 05A15 | Exact enumeration problems, generating functions |
References:
| [1] | Shkredov, I. D., Some applications of W. Rudin’s inequality to problems of combinatorial number theory, Unif. Distrib. Theory, 6, 2, 95-116 (2011) · Zbl 1313.11032 |
| [2] | Konyagin, S. V., On the estimate of the \(L_1\)-norm of an exponential sum, Approximation Theory of Functions and Operators Abstracts of the International Conference Dedicated to the 80th Anniversary of S. B. Stechkin, 0, 88-89 (2000) |
| [3] | Schoen, T.; Shkredov, I. D., On sumsets of convex sets, Combin. Probab. Comput., 20, 5, 793-798 (2011) · Zbl 1306.11013 · doi:10.1017/S0963548311000277 |
| [4] | Schoen, T.; Shkredov, I. D., Higher moments of convolutions, J. Number Theory, 133, 5, 1693-1737 (2013) · Zbl 1300.11018 · doi:10.1016/j.jnt.2012.10.010 |
| [5] | Shkredov, I. D., Some new results on higher energies, Trans. Moscow Math. Soc., 74, 31-63 (2013) · Zbl 1382.11016 · doi:10.1090/S0077-1554-2014-00212-0 |
| [6] | Olmezov, K. I.; Semchankau, A. S.; Shkredov, I. D., On Popular Sums and Differences for Sets with Small Multiplicative Doubling, Math. Notes, 108, 4, 557-565 (2020) · Zbl 1453.11020 · doi:10.1134/S000143462009028X |
| [7] | Shkredov, I. D., On sums of Szemerédi-Trotter sets, Proc. Steklov Inst. Math., 289, 300-309 (2015) · Zbl 1383.11014 · doi:10.1134/S0081543815040185 |
| [8] | Murphy, B.; Rudnev, M.; Shkredov, I. D.; Shteinikov, Y. N., On the Few Products, Many Sums Problem (2017) |
| [9] | Shkredov, I. D., Fourier analysis in combinatorial number theory, Russian Math. Surveys, 65, 3, 513-567 (2010) · Zbl 1270.11010 · doi:10.1070/RM2010v065n03ABEH004681 |
| [10] | Sidorenko, A., A correlation inequality for bipartite graphs, Graphs Combin., 9, 2, 201-204 (1993) · Zbl 0777.05096 · doi:10.1007/BF02988307 |
| [11] | Hatami, H., Graph norms and Sidorenko’s conjecture, Israel J. Math., 175, 125-150 (2010) · Zbl 1227.05183 · doi:10.1007/s11856-010-0005-1 |
| [12] | Conlon, D.; Fox, J.; Sudakov, B., An approximate version Sidorenko’s conjecture, Geom. Funct. Anal., 20, 6, 1354-1366 (2010) · Zbl 1228.05285 · doi:10.1007/s00039-010-0097-0 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
