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arXiv · 1208.2344

Some new inequalities in additive combinatorics

I. D. Shkredov
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Abstract

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.

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I. D. Shkredov. 2012-11-06. Some new inequalities in additive combinatorics. https://arxiv.org/abs/1208.2344

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