Algebra & Number Theory

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

Christian Kassel and Christophe Reutenauer

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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.

Article information

Algebra Number Theory, Volume 8, Number 2 (2014), 497-511.

Received: 25 April 2013
Revised: 15 July 2013
Accepted: 24 July 2013
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 68Q70: Algebraic theory of languages and automata [See also 18B20, 20M35] 68R15: Combinatorics on words
Secondary: 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 14H05: Algebraic functions; function fields [See also 11R58] 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture)

noncommutative formal power series language zeta function algebraic function


Kassel, Christian; Reutenauer, Christophe. Algebraicity of the zeta function associated to a matrix over a free group algebra. Algebra Number Theory 8 (2014), no. 2, 497--511. doi:10.2140/ant.2014.8.497.

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