The horocycle flow at prime times

Peter Sarnak, Adrián Ubis

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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 languageEnglish (US)
Pages (from-to)575-618
Number of pages44
JournalJournal des Mathematiques Pures et Appliquees
Issue number2
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Horocycle orbits
  • Joinings
  • Quantitative equidistribution
  • Ramanujan Conjectures
  • Sums over primes


Dive into the research topics of 'The horocycle flow at prime times'. Together they form a unique fingerprint.

Cite this