Depth reduction of a class of Witten zeta functions

TL;DR

This paper demonstrates a method to reduce the depth of certain Witten zeta functions associated with sl(4), expressing complex functions in terms of simpler, lower-argument functions based on parity conditions.

Contribution

It introduces a novel depth reduction technique for Witten zeta functions of sl(4) under specific parity constraints, expanding understanding of their structure.

Findings

Witten zeta functions with specific parameters can be expressed in terms of functions with fewer arguments.

Parity conditions on parameters enable depth reduction.

The method simplifies the analysis of these zeta functions.

Abstract

We show that if a,b,c,d,f are positive integers such that a+b+c+d+f is even, then the Witten zeta value zeta_{sl(4)}(a,b,c,d,0,f) is expressible in terms of Witten zeta functions with fewer arguments.