Small Gál sums and applications - Archive ouverte HAL
Article Dans Une Revue Journal of the London Mathematical Society Année : 2021

Small Gál sums and applications

Résumé

In recent years, maximizing Gál 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 Gál type, with respect to the L1-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.
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Dates et versions

hal-04753660 , version 1 (12-12-2024)

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Régis de la Bretèche, Marc Munsch, Gérald Tenenbaum. Small Gál sums and applications. Journal of the London Mathematical Society, 2021, 103 (1), pp.336-352. ⟨10.1112/jlms.12378⟩. ⟨hal-04753660⟩
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