49 research outputs found
Some new inequalities in additive combinatorics
In the paper we find new inequalities involving the intersections of shifts of some subset 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