The real parts of the nontrivial Riemann zeta function zeros

TL;DR

This paper presents a theorem concerning the real parts of nontrivial zeros of the Riemann zeta function, leveraging properties of holomorphic functions and rational functions near singularities.

Contribution

It introduces a new theoretical result about the possible values of the real parts of the zeros of the Riemann zeta function.

Findings

The real parts of nontrivial zeros can be characterized using holomorphic function properties.

Near singularities, the real part of certain rational functions can be arbitrarily assigned.

The theorem provides insights into the distribution of zeros of the zeta function.

Abstract

This theorem is based on holomorphy of studied functions and the fact that near a singularity point the real part of some rational function can take an arbitrary preassigned value.