Small G\'al sums and applications
Abstract
In recent years, maximizing G\'al sums regained interest due to a firm link with large values of -functions. In the present paper, we initiate an investigation of small sums of G\'al type, with respect to the -norm. We also consider the intertwined question of minimizing weighted versions of the usual multiplicative energy. We apply our estimates to: (i) a logarithmic refinement of Burgess' bound on character sums, improving previous results of Kerr, Shparlinski and Yau; (ii) an improvement on earlier lower bounds by Louboutin and the second author for the number of non vanishing theta functions associated to Dirichlet characters; and (iii) new lower bounds for low moments of character sums.
Cite
@article{arxiv.1906.12203,
title = {Small G\'al sums and applications},
author = {Régis de la Bretèche and Marc Munsch and Gérald Tenenbaum},
journal= {arXiv preprint arXiv:1906.12203},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1812.03788