Some new inequalities in additive combinatorics

By Ilya D. Shkredov. 2012

59 citations recorded by the source corpus.

In the paper we find new inequalities involving the intersections $A\cap (A-x)$ of shifts of some subset $A$ from an abelian group. We apply the inequalities to obtain new upper bounds for the additive energy of multiplicative subgroups and convex sets and also a series another results on the connection of the additive energy and so--called higher moments of convolutions. Besides we prove new theorems on multiplicative subgroups concerning lower bounds for its doubling constants, sharp lower bound for the cardinality of sumset of a multiplicative subgroup and its subprogression and another results.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e28fdde0463ba41fa54f30f3c93cc6256834ebee

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

On asymptotic formulae in some sum–product questions (2018, methodology): “(44) I. D. Shkredov 13 We need a result on the energy of a set which is obtained using the eigenvalues method, see [46], [47], [36], [37].”
On sum sets of sets having small product set (2015, background): “references in paper [11] (sharper bounds for difference of two sets, having small multiplicative doubling can be found in [8]).”