Zero free regions for Dirichlet series

Mathematics – Number Theory

Scientific paper

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Scientific paper

In this paper, we are interested in explicit zero-free discs for some
Dirichlet series and we also study a general Beurling-Nyman criterion for
$L$-functions. Our results generalize and improve previous results obtained by
N. Nikolski and by A. de Roton. As a concrete application, we get, for example,
a Beurling-Nyman type criterion for the Siegel zero problem.

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