On the value-distribution of the difference between logarithms of two symmetric power $L$-functions

TL;DR

This paper investigates the distribution of the difference between the logarithms of two symmetric power L-functions at a specific point, providing explicit integral representations of their average values.

Contribution

It introduces a novel explicit density function to describe the value distribution of these L-function differences at s > 1/2.

Findings

Derived explicit integral formulas for average value distributions.

Established the existence of a density function describing the distribution.

Provided analytical tools for studying symmetric power L-functions.

Abstract

We consider the value distribution of the difference between logarithms of two symmetric power $L$-functions at $s=\sigma > 1/2$. We prove that certain averages of those values can be written as integrals involving a density function which is constructed explicitly.