Large gaps between consecutive zeros of the Riemann zeta-function

TL;DR

This paper improves the known bounds on large gaps between zeros of the Riemann zeta-function by exploring new mollifier coefficients, assuming GRH, and demonstrating infinitely many gaps exceeding 3.033 times the average spacing.

Contribution

It introduces new mollifier coefficients that enhance the lower bounds on large gaps between zeros of the Riemann zeta-function under GRH.

Findings

Existence of infinitely many gaps > 3.033 times the average spacing

Improved bounds on large gaps assuming GRH

Methodology involving optimized mollifiers

Abstract

Combining the mollifiers, we exhibit other choices of coefficients that improve the results on large gaps between the zeros of the Riemann zeta-function. Precisely, assuming the Generalized Riemann Hypothesis (GRH), we show that there exist infinitely many consecutive gaps greater than 3.033 times the average spacing.