论文信息 - Sum-Product Inequalities with Perturbation - 字舞流文

Sum-Product Inequalities with Perturbation

Abstract Let A be a set of n > n 0(ε) positive real numbers, all at least 1 apart. We show that if δ a,b and are arbitrary real numbers satisfying and , we have .

Spencer Backman | Derrick Hart | Ernie Croot | Mariah Hamel

[1] Noga Alon,et al. An Application of Graph Theory to Additive Number Theory , 1985, Eur. J. Comb..

[2] L. A S Z L,et al. Crossing Numbers and Hard Erdős Problems in Discrete Geometry , 1997 .

[3] József Solymosi,et al. On the Number of Sums and Products , 2005 .

[4] L. A. Oa,et al. Crossing Numbers and Hard Erd} os Problems in Discrete Geometry , 1997 .

[5] Kevin Ford,et al. Sums and Products from a Finite Set of Real Numbers , 1998 .

[6] Melvyn B. Nathanson,et al. On sums and products of integers , 1997 .

[7] László A. Székely,et al. Crossing Numbers and Hard Erdős Problems in Discrete Geometry , 1997, Combinatorics, Probability and Computing.

[8] Sums and Products from a Finite Set of Real Numbers , 1998 .

[9] Yong-Gao Chen,et al. On sums and products of integers , 1999 .

[10] József Solymosi,et al. Bounding multiplicative energy by the sumset , 2009 .

[11] On the size of k-fold sum and product sets of integers , 2003, math/0309055.

[12] J. Solymosi. On sum-sets and product-sets of complex numbers , 2005 .

[13] Jozsef Solymosi. An upper bound on the multiplicative energy , 2008 .

[14] Endre Szemerédi,et al. Extremal problems in discrete geometry , 1983, Comb..