Large values of Dirichlet polynomials and zero density estimates for the Riemann zeta function

TL;DR

This paper provides new estimates for large values of Dirichlet polynomials, leading to improved zero density bounds for the Riemann zeta function, advancing understanding of its zeros.

Contribution

It introduces novel bounds for Dirichlet polynomial values, resulting in refined zero density estimates for the Riemann zeta function.

Findings

Improved bounds on large values of Dirichlet polynomials

Enhanced zero density estimates for the Riemann zeta function

Small but significant improvement over previous results of Bourgain and Jutila

Abstract

In this paper we obtain some new estimates for the number of large values of Dirichlet polynomials. Our results imply new zero density estimates for the Riemann zeta function which give a small improvement on results of Bourgain and Jutila.