On the distribution of large values of $|\zeta(1+{\rm i}t)|$

TL;DR

This paper investigates the distribution of large values of the Riemann zeta function on the 1-line, providing an improved density function that aligns with previous results by Granville and Soundararajan.

Contribution

It introduces an improved density function for large values of |z(1+it)|, enhancing understanding of its distribution on the 1-line.

Findings

Enhanced density function for large zeta values

Alignment with Granville and Soundararajan's range

Deeper insight into zeta function behavior on the 1-line

Abstract

In this article, we study the distribution of large values of the Riemann zeta function on the 1-line. We obtain an improved density function concerning large values, holding in the same range as that given by Granville and Soundararajan.