A remark on density theorems for Riemann's zeta-function

Abstract

The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann zeta function which are sufficiently strong to break the density hypothesis in a nontrivial part of the critical strip. Apart from a simple but ingenious idea of Halasz the proof uses only classical knowledge about the zeta function, results known since at least hundred years.

The paper is accepted for publication in SCIENCE CHINA Mathematics