English

Intersections of multiplicative subgroups and Heilbronn's exponential sum

Number Theory 2015-05-07 v3 Combinatorics

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.

Keywords

Cite

@article{arxiv.1302.3839,
  title  = {Intersections of multiplicative subgroups and Heilbronn's exponential sum},
  author = {Ilya D. Shkredov and Elena V. Solodkova and Ilya V. Vyugin},
  journal= {arXiv preprint arXiv:1302.3839},
  year   = {2015}
}

Comments

22 pages

R2 v1 2026-06-21T23:27:05.087Z