The conditional convergence of the Dirichlet series of an L-function

TL;DR

This paper explores the conditions under which the Dirichlet series associated with an L-function converges, using the Dirichlet divisor problem as a model to formulate a conjecture.

Contribution

It introduces a new conjecture about the conditional convergence of L-function Dirichlet series based on insights from the Dirichlet divisor problem.

Findings

Proposes a conjecture linking Dirichlet divisor problem to L-function series convergence

Provides a theoretical framework for understanding convergence conditions

Suggests avenues for future research in analytic number theory

Abstract

The Dirichlet divisor problem is used as a model to give a conjecture concerning the conditional convergence of the Dirichlet series of an L-function.