On Asymptotic Formula for the First Moment of the Riemann Zeta-Function on the Critical Line

TL;DR

This paper proves an asymptotic formula for the first moment of the Riemann zeta-function on the critical line assuming the Riemann Hypothesis, advancing understanding of its behavior.

Contribution

It provides a new asymptotic formula for the first moment of the zeta-function on the critical line under the Riemann Hypothesis, which was previously unproven.

Findings

Asymptotic formula established for the first moment

Results depend on the Riemann Hypothesis being true

Progress towards understanding the distribution of zeros

Abstract

In the present paper the asymptotic formulae for the first moment of the Riemann zeta-function on the critical line is proven under assumption of the Riemann Hypothesis.