Transcendence of the Artin-Mazur Zeta Function for Polynomial Maps of A¹(F_p)

2012/02/02 by Andrew Bridy, Bridy, Andrew
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.NT #msc:11B85 #msc:37P05

paper · pdf · doi:10.48550/arxiv.1202.0362

10 pages, 1 figure

arxiv created 2012/05/14 · arxiv updated 2012/05/15

Abstract

We study the rationality of the Artin-Mazur zeta function of a dynamical system defined by a polynomial self-map of A¹(k), where k is the algebraic closure of the finite field F_p. The zeta functions of the maps f(x)=x^m for (p,m)=1 and f(x)=x^pm+ax for nonzero a in F_p^m, p odd, are shown to be transcendental.

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