# On the zeros of sum from n=1 to 00 of lambda_P(n)/n^s

## TL;DR

This paper constructs a Dirichlet series with a unique zero in its half-plane of convergence and explores conditions related to the Generalized Riemann Hypothesis, addressing a question posed by Michel Balazard.

## Contribution

It provides a specific Dirichlet series with a single zero and proposes new sufficient conditions for the Generalized Riemann Hypothesis.

## Key findings

- Constructed a Dirichlet series with only one zero in its half-plane
- Proposed several sufficient conditions for the Generalized Riemann Hypothesis
- Addressed a question of Michel Balazard

## Abstract

Our main result is to answer a question of Michel Balazard by giving a Dirichlet series with only one zero in its half-plane of convergence. At the end of the paper we also give several sufficient conditions for the Generalized Riemann Hypothesis and ask if any of them are true.