Gaps between zeros of the Riemann zeta-function

TL;DR

This paper proves the existence of infinitely many large gaps between consecutive zeros of the Riemann zeta-function on the critical line, exceeding 3.18 times the average spacing, and explores larger gaps for multiple zeros.

Contribution

It introduces a method to demonstrate infinitely many large gaps between zeros and extends to larger gaps for multiple zeros if they exist.

Findings

Existence of infinitely many zeros with gaps > 3.18 times average

Method modification to find larger gaps for multiple zeros

Potential implications for zeros' distribution on the critical line

Abstract

We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than $3.18$ times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the zeta function on the critical line (if such zeros exist).