Sommes de Gál et applications

2018/04/04 by de la Bretèche, Régis, Tenenbaum, Gérald · 3 citations
#11A05 #11L40 #11M06 #11N25 #11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1804.01629

Abstract

We evaluate the asymptotic size of various sums of Gál type, in particular S( M):=∑_m,n\inM √((m,n) \over [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|= N}S( M)/N) and derive new lower bounds for localized extreme values of the Riemann zeta-function, for extremal values of some Dirichlet L-functions at s=1/2, and for large character sums.

Cited by

• Extreme values of quadratic Dirichlet L-functions with prime-related moduli
• The metric theory of small gaps for a sequence of real numbers
• Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field

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• Refinements of Gál's theorem and applications
• Large zeta sums
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• The maximum size of short character sums
• The typical size of character and zeta sums is o(√(x))