Pedro Ribeiro, Semyon Yakubovich
Published 2021-12-20, updated 2022-02-24Version 2
By generalizing the classical Selberg-Chowla formula, we establish the analytic continuation and functional equation for a large class of Epstein zeta functions. This continuation is studied in order to provide new classes of theorems regarding the distribution of zeros of Dirichlet series in their critical lines and to produce a new method for the study of these problems. Due to the symmetries provided by the representation via the Selberg-Chowla formula, some generalizations of well-known formulas in analytic number theory are also deduced as examples.
Comments: typos corrected; added corollary 4.5 and example 5.6
Dirichlet series constructed from periods of automorphic forms
The Lerch's $Φ$ Analytic Continuation
Analytic Continuation of some zeta functions
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