Moments of the Riemann zeta-function at its relative extrema on the critical line

TL;DR

This paper derives nearly matching upper and lower bounds for the moments of the Riemann zeta-function at its extreme values on the critical line, assuming the Riemann hypothesis, advancing understanding of its behavior at zeros.

Contribution

It provides new bounds for moments of the zeta-function at its extrema on the critical line, assuming the Riemann hypothesis, using bounds for derivatives of the zeta-function.

Findings

Bounds are nearly of the same order of magnitude.

Assumes the Riemann hypothesis for results.

Uses bounds for derivatives of the zeta-function.

Abstract

Assuming the Riemann hypothesis, we obtain upper and lower bounds for moments of the Riemann zeta-function averaged over the extreme values between its zeros on the critical line. Our bounds are very nearly the same order of magnitude. The proof requires upper and lower bounds for continuous moments of derivatives of Riemann zeta-function on the critical line.