A Necessary Condition for a Nontrivial Zero of the Riemann Zeta Function via the Polylogarithmic Function

TL;DR

The paper discusses a necessary condition for nontrivial zeros of the Riemann zeta function using polylogarithmic functions, but an error in the original derivation affects its conclusions.

Contribution

The paper attempts to establish a new necessary condition for Riemann zeta zeros via polylogarithmic functions, though an error impacts its validity.

Findings

Error identified in the residue calculation

Function $Z(s,x)$ is regular at $x=1$

Original results are invalidated by the mistake

Abstract

The author has found today an error in the denominator of the residue equation (4.5). This unfortunate mistake makes the conclusions and the title of the paper incorrect. The function $Z(s,x)$ is regular at $x=1$ and the multivalued part disappears. The original motivation of the paper was to derive an old (and correct!) result due to the author using a different approach.