The horocycle flow at prime times

Peter Sarnak; Adrián Ubis

doi:10.1016/j.matpur.2014.07.004

The horocycle flow at prime times

Peter Sarnak, Adrián Ubis

Mathematics

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

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 GL2/Q. In the process, we derive an effective version of Dani's Theorem for the (discrete) horocycle flow.

Original language	English (US)
Pages (from-to)	575-618
Number of pages	44
Journal	Journal des Mathematiques Pures et Appliquees
Volume	103
Issue number	2
DOIs	https://doi.org/10.1016/j.matpur.2014.07.004
State	Published - 2015

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Horocycle orbits
Joinings
Quantitative equidistribution
Ramanujan Conjectures
Sums over primes

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10.1016/j.matpur.2014.07.004

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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 GL2/Q. In the process, we derive an effective version of Dani's Theorem for the (discrete) horocycle flow.",

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AU - Ubis, Adrián

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AB - 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 GL2/Q. In the process, we derive an effective version of Dani's Theorem for the (discrete) horocycle flow.

KW - Horocycle orbits

KW - Joinings

KW - Quantitative equidistribution

KW - Ramanujan Conjectures

KW - Sums over primes

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 2

ER -

The horocycle flow at prime times

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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