On tripling constant of multiplicative subgroups
Number Theory
2015-04-20 v1 Combinatorics
Abstract
We prove that any multiplicative subgroup G of the prime field f_p with |G| < p^{1/2} satisfies |3G| \gg |G|^2 / \log |G|. Also, we obtain a bound for the multiplicative energy of any nonzero shift of G, namely E^* (G+x) \ll |G|^2 log |G|, where x is an arbitrary nonzero residue.
Cite
@article{arxiv.1504.04522,
title = {On tripling constant of multiplicative subgroups},
author = {Ilya D. Shkredov},
journal= {arXiv preprint arXiv:1504.04522},
year = {2015}
}
Comments
8 pages