The horocycle flow at prime times

Details The horocycle flow at prime times The horocycle flow at prime times

2011-10-04

arxiv.org/abs/1110.0777v2

Mathematics

Number Theory

52 pages, 2 figures, submitted. Remark added after Theorem 1.1, some minor typos corrected and more precise bounds added at th

Scientific paper

We prove that the orbit of a generic 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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