4.2 Article

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

Journal

ALGEBRA & NUMBER THEORY
Volume 8, Issue 2, Pages 497-511

Publisher

MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/ant.2014.8.497

Keywords

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

Categories

Funding

  1. Laboratoire International Franco-Quebecois de Recherche en Combinatoire (LIRCO)
  2. Universite du Quebec a Montreal (UQAM)
  3. NSERC (Canada)

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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.

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