Triple mean values of Witten $L$-functions

TL;DR

This paper investigates the mean values of Witten $L$-functions in the character aspect, providing formulas for first and second moments and explicitly calculating the cubic moment for $SU(2)$.

Contribution

It introduces explicit formulas for mean values of Witten $L$-functions and computes the cubic moment for $SU(2)$, advancing understanding of their statistical properties.

Findings

Derived general formulas for mean values with first and second powers.

Explicitly calculated the cubic moment for $SU(2)$.

Enhanced understanding of the distribution of Witten $L$-functions.

Abstract

Mean values of Witten $L$-functions in the "character" aspect are investigated. After giving a general formula for mean values with the first and the second power, we explicitly calculate the cubic moment for $SU(2)$.