On exponential sums over multiplicative subgroups of medium size
Number Theory
2013-11-25 v1 Combinatorics
Abstract
In the paper we obtain some new upper bounds for exponential sums over multiplicative subgroups G of F^*_p having sizes in the range [p^{c_1}, p^{c_2}], where c_1,c_2 are some absolute constants close to 1/2. As an application we prove that in symmetric case G is always an additive basis of order five, provided by |G| > p^{1/2} log^{1/3} p. Also the method allows us to give a new upper bound for Heilbronn's exponential sum.
Cite
@article{arxiv.1311.5726,
title = {On exponential sums over multiplicative subgroups of medium size},
author = {Ilya D. Shkredov},
journal= {arXiv preprint arXiv:1311.5726},
year = {2013}
}
Comments
14 pages