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

TL;DR

This paper studies how often the Riemann zeta function attains large values in the critical strip between 1/2 and 1, providing an improved distribution function for these large values.

Contribution

It offers an improved distribution function for large values of |z(6+ t)| in the critical strip, extending previous results by Lamzouri.

Findings

Derived an enhanced distribution function for large zeta values.

Extended the understanding of zeta function behavior in the critical strip.

Provides sharper estimates for the frequency of large zeta values.

Abstract

We investigate the distribution of large values of the Riemann zeta function $\zeta(s)$ in the strip $1/2<\re s<1$. For any fixed $\re s=\sigma\in(1/2,1)$, we obtain an improved distribution function of large values of $|\zeta(\sigma+\i t)|$, holding in the same range as that given by Lamzouri.