A Note on the Zero-Free Regions of the Zeta Function

TL;DR

This paper identifies a new zero-free region for the Riemann zeta function, specifically where the real part of s exceeds 21/40, advancing understanding of its zeros.

Contribution

It establishes a novel zero-free region for the zeta function with Re(s) > 21/40, improving previous bounds.

Findings

Zero-free region established at Re(s) > 21/40

Enhances understanding of zeta function zeros

Potential implications for prime number theory

Abstract

This short note contributes a new zero-free region of the zeta function. This zero-free region has the form {s : Re(s) > a}, where a = 21/40.