An equation satisfied by all non-trivial zeros $\rho$ of the Riemann zeta function $\zeta$

Abstract

We show that if $\rho$ is a non-trivial zero of the Riemann zeta function $\zeta$ then $$2^{\rho }+\frac{1}{\rho -1}+1/2=\rho {\int }_1^{\infty }t+1/2t^{-\rho -1}dt$$ where, $x$ is the fractional part of $x$.

arXiv comment3 pages