Large gaps between consecutive maxima of the Riemann zeta-function on the critical line

TL;DR

This paper establishes new lower bounds for the normalized gaps between consecutive maxima of the Riemann zeta-function on the critical line, assuming the Riemann hypothesis, using advanced inequalities.

Contribution

It introduces a novel approach combining Sobolev and Opial inequalities with optimal constants to analyze maxima gaps under the Riemann hypothesis.

Findings

Derived new lower bounds for maxima gaps

Applied Sobolev and Opial inequalities with best constants

Results depend on the truth of the Riemann hypothesis

Abstract

In this paper, we derive new lower bounds for the normalized distances between consecutive maxima of the Riemann zeta-function on the critical line subject to the truth of the Riemann hypothesis. The method of our proofs relies on a Sobolev type inequality of one dimension and an Opial type inequality with best possible constants.