Joint value distribution of $L$-functions on the critical line

TL;DR

This paper investigates the joint distribution of $L$-functions on the critical line, providing large deviation results and mean value theorems that suggest these functions behave independently in a statistical sense.

Contribution

It introduces new joint large deviation results and mean value theorems for $L$-functions, advancing understanding of their statistical independence.

Findings

Joint large deviations established for $L$-functions.

Mean value theorems support statistical independence.

Evidence of normal distribution behavior in $L$-function values.

Abstract

In this paper, we discuss the joint value distribution of $L$-functions in a suitable class. We obtain joint large deviations results in the central limit theorem for these $L$-functions and some mean value theorems, which give evidence that different $L$-functions are "statistically independent".