Riemann's Auxiliary Function. Right limit of zeros

TL;DR

The paper investigates the zeros of Riemann's auxiliary function, providing evidence that their real parts are less than 1 for very high imaginary parts, and conjectures this holds universally.

Contribution

It proves that zeros with extremely high imaginary parts have real parts less than 1, supporting the conjecture for all zeros of the auxiliary Riemann function.

Findings

Zeros with Im > 3.9211...×10^{65} have Re < 1

Numerical data supports the conjecture for all zeros

Supports the hypothesis that all zeros satisfy Re < 1

Abstract

Numerical data suggest that the zeros $\rho$ of the auxiliary Riemann function in the upper half-plane satisfy $\mathop{\mathrm{Re}}(\rho)<1$. We show that this is true for those zeros with $\mathop{\mathrm{Im}}(\rho)> 3.9211\dots10^{65}$. We conjecture that this is true for all of them.