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arXiv · 2205.11408

Zeros of dynamical zeta functions for hyperbolic quadradic maps

Yuqiu Fu
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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 $1/2 +$, that is, for every $\epsilon > 0$, there exist only finitely many zeros in the strip $\mathrm{Re}(s) > 1/2 + \epsilon$. We also present some numerical plots of zeros of $Z(s)$ using the method proposed in Jenkinson-Pollicott.

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Yuqiu Fu. 2022-05-23. Zeros of dynamical zeta functions for hyperbolic quadradic maps. https://doi.org/10.2140/paa.2024.6.633

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