A one-formula proof of the nonvanishing of L-functions of real characters at 1

TL;DR

This paper provides a straightforward analytic proof demonstrating that L-functions associated with real non-principal Dirichlet characters do not vanish at 1, confirming a key property in number theory.

Contribution

It introduces a simple, one-formula proof for the nonvanishing of these L-functions at 1, simplifying previous approaches.

Findings

L-functions of real non-principal Dirichlet characters are nonzero at 1

The proof is simpler and more direct than previous methods

Confirms a fundamental property in analytic number theory

Abstract

We present a simple analytic proof that L-functions of real non-principal Dirichlet characters are nonzero at 1.