Exponential moments of the argument of the Riemann zeta function on the critical line

TL;DR

This paper establishes an upper bound for the exponential moments of the imaginary part of the logarithm of the Riemann zeta function on the critical line, assuming the Riemann hypothesis, shedding light on zero distribution fluctuations.

Contribution

It provides a new upper bound for exponential moments of the zeta function's argument, matching prior results in accuracy under the Riemann hypothesis.

Findings

Upper bound for exponential moments derived

Results align with Soundararajan's previous findings

Enhances understanding of zero distribution fluctuations

Abstract

In this article, we give, under the Riemann hypothesis, an upper bound for the exponential moments of the imaginary part of the logarithm of the Riemann zeta function on the critical line. Our result, which gives information on the fluctuations of the distribution of the zeros of $\zeta$, has the same accuracy as the result obtained by Soundararajan in his paper entitled "Moments of the Riemann zeta function".