The quantum variance of the modular surface

P. Sarnak, P. Zhao, M. Woodbury

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The variance of observables of quantum states of the Laplacian on the modular surface is calculated in the semiclassical limit. It is shown that this hermitian form is diagonalized by the irreducible representations of the modular quotient and on each of these it is equal to the classical variance of the geodesic flow after the insertion of a subtle arithmetical special value of the corresponding L-function.

Original languageEnglish (US)
Pages (from-to)1155-1200
Number of pages46
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Issue number5
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • General Mathematics


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