Vol. 8, No. 2, 2014

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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
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