A new approach to gaps between zeta zeros

TL;DR

This paper investigates the distribution of zeros of the Riemann zeta function, providing new insights into small gaps between zeros and exploring their behavior under the alternative hypothesis.

Contribution

It introduces a novel approach to studying gaps between zeta zeros and analyzes their distribution using Dirichlet polynomials on the critical line.

Findings

Proves a corollary on small gaps between zeta zeros

Examines zero distribution under the alternative hypothesis

Proposes a new method for analyzing zero gaps

Abstract

We study the value-distribution of Dirichlet polynomials on the critical line $\Re(s)=\tfrac{1}{2}$. As a consequence, we prove a corollary on small consecutive gaps between zeros of the Riemann zeta function. We also examine the distribution of zeros under the so-called alternative hypothesis and present a new approach to the problem of gaps between the zeros.