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

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.

arXiv comment13 pages; Versions 2 and 3: minor corrections. Versions 4 and 5: References [12], [19] added