Algebraicity of the zeta function associated to a matrix over a free group algebra

TL;DR

This paper proves that the zeta function associated with matrices over a ring of noncommutative Laurent polynomials is algebraic, extending Kontsevich's construction.

Contribution

It generalizes Kontsevich's construction by showing the algebraicity of the zeta function for matrices over noncommutative Laurent polynomial rings.

Findings

Zeta function is algebraic for matrices over noncommutative Laurent polynomial rings

Generalizes previous constructions by Kontsevich

Establishes algebraicity in a noncommutative setting

Abstract

Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coefficients. We show that such a zeta function is an algebraic function.