Zeta Functions of Polynomial Dynamics on the Algebraic Closure of a Finite Field

Details Zeta Functions of Polynomial Dynamics on the Algebraic Closure of a Finite Field Zeta Functions of Polynomial Dynamics on the Algebraic Closure of a Finite Field

2012-02-02

arxiv.org/abs/1202.0362v1

Mathematics

Number Theory

10 pages, 1 figure

Scientific paper

We study the rationality of the Artin-Mazur zeta function of a dynamical
system defined by a polynomial map on 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^p+ax for
nonzero a in F_p are shown to be transcendental.

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