Discrete mean square of the Riemann zeta-function over imaginary parts of its zeros

TL;DR

Under the assumption of the Riemann hypothesis, the paper derives an asymptotic formula for the discrete mean square of the Riemann zeta-function evaluated at the imaginary parts of its zeros, specifically on the right side of the critical strip.

Contribution

The paper provides a new asymptotic formula for the discrete mean square of the zeta-function over zeros' imaginary parts, advancing understanding of its behavior under the Riemann hypothesis.

Findings

Asymptotic formula for the discrete mean square derived

Results apply on the right-hand side of the critical strip

Supports conjectures about zeta-function behavior at zeros

Abstract

Assume the Riemann hypothesis. On the right-hand side of the critical strip, we obtain an asymptotic formula for the discrete mean square of the Riemann zeta-function over imaginary parts of its zeros.