@techreport{62e6819810134e6a871dc19fe758d13b,
title = "Small G{\'a}l sums and applications",
abstract = " In recent years, maximizing G\'al sums regained interest due to a firm link with large values of $L$-functions. In the present paper, we initiate an investigation of small sums of G\'al type, with respect to the $L^1$-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. ",
keywords = "math.NT, 11L40, 11N37 (Primary), 05D05, 11F27 (Secondary)",
author = "Bret{\`e}che, {R{\'e}gis de la} and Marc Munsch and G{\'e}rald Tenenbaum",
note = "arXiv admin note: text overlap with arXiv:1812.03788",
year = "2019",
month = jun,
day = "27",
language = "English",
series = "arXiv.org e-Print archive",
publisher = "Cornell University Library",
type = "WorkingPaper",
institution = "Cornell University Library",
}