Algebraicity of the zeta function associated to a matrix over a free group algebra
Combinatorics
2014-09-02 v5 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.1303.3481,
title = {Algebraicity of the zeta function associated to a matrix over a free group algebra},
author = {Christian Kassel and Christophe Reutenauer},
journal= {arXiv preprint arXiv:1303.3481},
year = {2014}
}
Comments
13 pages; Versions 2 and 3: minor corrections. Versions 4 and 5: References [12], [19] added