Algebra Number Theory 8-2 (2014), 497-511, doi:10.2140/ant.2014.8.497 - arXiv:1303.3481

Christian Kassel and Christophe Reutenauer

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

Mathematics Subject Classification (2000): Primary 05A15, 14G10, 68Q70, Secondary 05E15, 68R15, 20M35, 14H05

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.

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(21 octobre 2014)