One metric result about analytic continuation of some Dirichlet series

In this paper we consider certain 1-parametric family of Dirichlet series. For a particular value of the parameter the series turns into the Dirichlet series for the Riemann zeta function. We prove that almost every series of the family has analytic continuation to the half plane Re s > 1/2 where...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2007-12
Main Author: Rezvyakova, Irina
Format: Article
Language:English
Subjects:
Dirichlet problem
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we consider certain 1-parametric family of Dirichlet series. For a particular value of the parameter the series turns into the Dirichlet series for the Riemann zeta function. We prove that almost every series of the family has analytic continuation to the half plane Re s > 1/2 where it doesn't vanish. The result was obtained before by different authors. We give its simple proof in terms of estimates of some trigonometric sums.
ISSN:2331-8422