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research
Some new inequalities in additive combinatorics
Authors
I. D. Shkredov
Publication date
6 November 2012
Publisher
View
on
arXiv
Abstract
In the paper we find new inequalities involving the intersections
A
β©
(
A
β
x
)
A\cap (A-x)
A
β©
(
A
β
x
)
of shifts of some subset
A
A
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.Comment: 39 page
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Last time updated on 30/10/2017