A discrete mean value of the derivative of the Riemann zeta function

TL;DR

This paper computes a discrete mean value of the derivative of the Riemann zeta function, which is crucial for understanding the behavior of its zeros and has implications for number theory.

Contribution

It introduces a new computation of the discrete mean value of ta'() at non-trivial zeros, advancing the analysis of the zeta function's zeros.

Findings

Derived a formula for the discrete mean value of ta'()

Provides insights into the size of ta'() at zeros

Enhances understanding of the distribution of zeta zeros

Abstract

In this article we compute a discrete mean value of the derivative of the Riemann zeta function. This mean value will be important for several applications concerning the size of $\zeta'(\rho)$ where $\zeta(s)$ is the Riemann zeta function and $\rho$ is a non-trivial zero of the Riemann zeta function.