Vol. 8, No. 2, 2014
Download this article
Download this article For screen
For printing
Recent Issues

Volume 19, 1 issue

Volume 18, 12 issues

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
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