The variance of arithmetic measures associated to closed geodesics on the modular surface

Wenzhi Luo, Zeév Rudnick, Peter Sarnak

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We determine the variance for the fluctuations of the arithmetic measures obtained by collecting all closed geodesics on the modular surface with the same discriminant and ordering them by the latter. This arithmetic variance differs by subtle factors from the variance that one gets when considering individual closed geodesics when ordered by their length. The arithmetic variance is the same one that appears in the fluctuations of measures associated with quantum states on the modular surface.

Original languageEnglish (US)
Pages (from-to)271-309
Number of pages39
JournalJournal of Modern Dynamics
Volume3
Issue number2
DOIs
StatePublished - Sep 28 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Keywords

  • Arithmetic variance
  • Closed geodesics
  • Modular surface

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