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arXiv · 1110.0777

The horocycle flow at prime times

P. Sarnak·A. Ubis
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Abstract

We prove that the orbit of a non-periodic point at prime values of the horocycle flow in the modular surface is dense in a set of positive measure. For some special orbits we also prove that they are dense in the whole space (assuming the Ramanujan/Selberg conjectures for GL(2)/Q). In the process, we derive an effective version of Dani's Theorem for the (discrete) horocycle flow.

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P. Sarnak, A. Ubis. 2014-06-02. The horocycle flow at prime times. https://arxiv.org/abs/1110.0777

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