Number variance for arithmetic hyperbolic surfaces

W. Luo, P. Sarnak

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


We prove that the number variance for the spectrum of an arithmetic surface is highly nonrigid in part of the universal range. In fact it is close to having a Poisson behavior. This fact was discovered numerically by Schmit, Bogomolny, Georgeot and Giannoni. It has its origin in the high degeneracy of the length spectrum, first observed by Selberg.

Original languageEnglish (US)
Pages (from-to)419-432
Number of pages14
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - Mar 1994

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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