On the Epstein zeta function and the zeros of a class of Dirichlet series

2021/12/20 by Pedro Ribeiro, Semyon Yakubovich, Ribeiro, Pedro +1 · 2 citations
Chemical Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT) #Thermodynamic properties of mixtures #math.CA #math.NT

paper · pdf · doi:10.48550/arxiv.2112.10561

typos corrected; added corollary 4.5 and example 5.6

openalex publication_date 2021/12/20 · arxiv created 2022/02/24 · arxiv updated 2022/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Number Field Analogue of Jacobi Theta Relation And Zeros of Dedekind zeta function on Re(s)=1/2
• Analogues of a formula of Ferrar: what I have learned from Semyon Yakubovich

Related

• An analogue of the Chowla-Selberg formula for several automorphic L-functions
• On the zeros of Epstein zeta functions
• On the zeros of Epstein zeta functions near the critical line
• The Epstein zeta-function contains a positive proportion of non-trivial zeros on the critical line
• Certain Extensions of Results of Siegel, Wilton and Hardy