Zero-free regions for Dirichlet series (II)

TL;DR

This paper advances the understanding of zero-free regions for Dirichlet series by removing technical conditions, enabling simpler descriptions and more practical applications of zero-free discs.

Contribution

It introduces two natural methods to eliminate technical conditions in zero-free region descriptions for Dirichlet series, simplifying their explicit characterization.

Findings

Two new methods to remove technical conditions

Simplified explicit zero-free regions

Enhanced applicability for direct use

Abstract

In this paper, we continue some work devoted to explicit zero-free discs for a large class of Dirichlet series. In a previous article, such zero-free regions were described using some spaces of functions which were defined with some technical conditions. Here we give two different natural ways in order to remove those technical conditions. In particular this allows to right down explicit zero-free regions differently and to obtain for them an easier description useful for direct applications.