# Artin-Mazur zeta function

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Let $\mathrm{Fix}(f^n)$ be the set of fixed points of the $n$th iterate $f^n$ of $f$. Let $\mathrm{Card}(\mathrm{Fix})(f^n)$ denote the cardinality of the set $\mathrm{Fix}(f^n)$. The Artin-Mazur zeta function is $$\zeta_f(z)=\exp \left( \displaystyle\sum_{k=1}^{\infty} \mathrm{Card}(\mathrm{Fix})[f^n] \dfrac{z^n}{n} \right).$$