# The error term in the prime orbit theorem for expanding semiflows

@article{Tsujii2015TheET, title={The error term in the prime orbit theorem for expanding semiflows}, author={Masato Tsujii}, journal={Ergodic Theory and Dynamical Systems}, year={2015}, volume={38}, pages={1954 - 2000} }

We consider suspension semiflows of angle-multiplying maps on the circle and study the distributions of periods of their periodic orbits. Under generic conditions on the roof function, we give an asymptotic formula on the number $\unicode[STIX]{x1D70B}(T)$ of prime periodic orbits with period $\leq T$ . The error term is bounded, at least, by $$\begin{eqnarray}\exp \biggl(\biggl(1-\frac{1}{4\lceil \unicode[STIX]{x1D712}_{\text{max}}/h_{\text{top}}\rceil }+\unicode[STIX]{x1D700}\biggr)h_{\text…

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