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math.NT2020
A pair correlation problem, and counting lattice points with the zeta function
Christoph Aistleitner, Daniel El-Baz, Marc Munsch
The pair correlation is a localized statistic for sequences in the unit interval. Pseudo-random behavior with respect to this statistic is called Poissonian behavior. The metric th…
math.NT2020
Second moment of Dirichlet -functions, character sums over subgroups and upper bounds on relative class numbers
Stéphane Louboutin, Marc Munsch
We prove an asymptotic formula for the mean-square average of - functions associated to subgroups of characters of sufficiently large size. Our proof relies on the study of cert…