The horocycle flow at prime times

By Peter Sarnak, A. Ubis. 2011

66 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca48dc61bf1555162bb5d8cafbe9f5192cf5530d

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In Algebra and Number Theory

1. J. Kułaga-Przymus
2. Mariusz Lemanczyk
3. Sébastien Ferenczi

In Discrete Mathematics and Combinatorics

1. J. Kułaga-Przymus
2. Mariusz Lemanczyk
3. Sébastien Ferenczi

In Mathematical Physics

1. J. Kułaga-Przymus
2. Mariusz Lemanczyk
3. Sébastien Ferenczi

Citations in the corpus

• Sarnak’s Conjecture: What’s New (2017, background): “Do we have a PNT for horocycle flows? For a partial answer, see [150], where it is proved that if Γx is a generic point for Haar measure μX of X then any limit point of ́ 1 πpNq ř pďN δTpΓx ̄ is a measure which is absolutely continuous with respect to μX .”
• Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures (2016, unknown): “CHOWLA AND SARNAK CONJECTURES 3 dynamical systems [1], [2], [3], [5], [6], [7], [8], [9], [12], [13], [14], [15], [17], [18], [25], [29], [33], [39], [40], [41], [42], [43], [48], [49], [52], [58]; for further variants of the Sarnak conjecture, see [10], [13], [37].”