Sommes de Gál et applications

By Régis de la Bretèche, Gerald Tenenbaum. Proceedings of the London Mathematical Society, 2018

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We evaluate the asymptotic size of various sums of Gál type, in particular S(M):=∑m,n∈M(m,n)[m,n],where M is a finite set of integers. Elaborating on methods recently developed by Bondarenko and Seip, we obtain an asymptotic formula for log sup|M|=NS(M)/Nand derive new lower bounds for localized extreme values of the Riemann zeta‐function, for extremal values of some Dirichlet L ‐functions at s=12 , and for large character sums.

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