The L-Functions Have Only Simple Non Trivial Zeros

TL;DR

This paper argues that non-trivial zeros of L-functions are necessarily simple, using conformal mapping and symmetry arguments near hypothetical double zeros, supporting the Riemann Hypothesis.

Contribution

It introduces a novel conformal mapping approach to demonstrate the impossibility of multiple non-trivial zeros of L-functions.

Findings

Double zeros of L-functions cannot exist.

Non-trivial zeros are necessarily simple.

Supports the Riemann Hypothesis.

Abstract

By using an analogy with the case of very close zeros symmetric with respect to the critical line of the Davenport and Heilbronn function, we study the conformal mapping of L-functions in a neighborhood of a hypothetical double zero and conclude that such a zero cannot exist. Keywords: Riemann Hypothesis, non trivial zeros, Ghisa's strips, Ghisa's fundamental domains, Ghisa's intertwined curves 2010 Mathematics Subject Classification: 30C35; 11M26