Note on the Zeros of a Dirichlet Function

TL;DR

This paper proves that non-trivial zeros of a certain analytically continued Dirichlet series cannot exist off the critical line, challenging long-standing presumptions in number theory.

Contribution

It provides a proof that non-trivial zeros off the critical line do not exist for a specific Dirichlet function, contradicting previous beliefs.

Findings

Non-trivial zeros off the critical line are proven not to exist.

The result challenges longstanding assumptions in the theory of Dirichlet series.

The proof has implications for the understanding of zeros of L-functions.

Abstract

The existence of non trivial zeros off the critical line for a function obtained by analytic continuation of a particular Dirichlet series is studied. Contrary to what has been presumed for a long time, we prove that such zeros cannot exist.