Riemann's Auxiliary Function. Right limit of zeros

Abstract

Numerical data suggest that the zeros $\rho$ of the auxiliary Riemann function in the upper half-plane satisfy $\mathrm{Re}(\rho )<1$. We show that this is true for those zeros with $\mathrm{Im}(\rho )>3.9211\dots 10^{65}$. We conjecture that this is true for all of them.

arXiv comment10 pages