Abstract

We prove that the dynamical zeta function $Z(s)$ associated to $z^2+c$ with $c<-3.75$ has essential zero-free strips of size $\frac{1}{2}+$ , that is, for every $𝜖>0$, there exist only finitely many zeros in the strip $\mathrm{Re}<!--FUNCTION\; APPLICATION-->(s)>\frac{1}{2}+𝜖$. We also present some numerical plots of zeros of $Z(s)$ based on the method proposed by Jenkinson and Pollicott (Amer. J. Math. 124 (2002), 495–545).

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