A short proof of Levinson's theorem

TL;DR

This paper presents a concise proof of Levinson's theorem, establishing that over one-third of the zeros of the Riemann zeta function lie on the critical line, contributing to the understanding of the distribution of zeros.

Contribution

It provides a shorter, more accessible proof of Levinson's theorem, improving upon previous lengthy demonstrations.

Findings

Confirmed that more than 1/3 of zeta zeros are on the critical line

Simplified the proof technique for Levinson's theorem

Enhanced understanding of zeros distribution of the zeta function

Abstract

We give a short proof of Levinson's result that more than 1/3 of the zeros of the zeta function are on the critical line.