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

Kassel, Christian; Reutenauer, Christophe

doi:10.2140/ant.2014.8.497

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

Christian Kassel and Christophe Reutenauer

Vol. 8 (2014), No. 2, 497–511

DOI: 10.2140/ant.2014.8.497

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

noncommutative formal power series, language, zeta function, algebraic function

Mathematical Subject Classification 2010

Primary: 05A15, 68Q70, 68R15

Secondary: 05E15, 14H05, 14G10

Milestones

Received: 25 April 2013

Revised: 15 July 2013

Accepted: 24 July 2013

Published: 18 May 2014

Authors

Christian Kassel
Institut de Recherche Mathématique Avancée, CNRS Université de Strasbourg 7 rue René Descartes 67084 Strasbourg France

Christophe Reutenauer
Mathématiques Université du Québec à Montréal CP 8888 succursale Centre Ville Montréal QC H3C 3P8 Canada

Vol. 8, No. 2, 2014