A discrete mean value of the Riemann zeta function

Kübra Benli, Ertan Elma, Nathan Ng

In this work, we estimate the sum \begin{align*} \sum_{0 < \Im(ρ) \leq T} ζ(ρ+α)X(ρ) Y(1\!-\! ρ) \end{align*} over the nontirival zeros $\rho$ of the Riemann zeta funtion where $\alpha$ is…