Intersections of multiplicative subgroups and Heilbronn's exponential sum

Abstract

The paper is devoted to some applications of Stepanov method. In the first part of the paper we obtain the estimate of the cardinality of the set, which is obtained as an intersection of additive shifts of some different subgroups of F^*_p. In the second part we prove a new upper bound for Heilbronn's exponential sum and obtain a series of applications of our result to distribution of Fermat quotients. Also we study additive decompositions of multiplicative subgroups.

22 pages

References in corpus (2)

• Some new inequalities in additive combinatorics
• On vanishing Fermat quotients and a bound of the Ihara sum

Cited by in corpus (3)

• An introduction to higher energies and sumsets
• Solutions of polynomial equation over ${\mathbb{F}}_p$ and new bounds of additive energy
• On tripling constant of multiplicative subgroups