Number variance for arithmetic hyperbolic surfaces

W. Luo; P. Sarnak

doi:10.1007/BF02099785

Number variance for arithmetic hyperbolic surfaces

W. Luo, P. Sarnak

Mathematics

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

39 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	419-432
Number of pages	14
Journal	Communications In Mathematical Physics
Volume	161
Issue number	2
DOIs	https://doi.org/10.1007/BF02099785
State	Published - Mar 1994

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02099785

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abstract = "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.",

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AB - 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.

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Number variance for arithmetic hyperbolic surfaces

Abstract

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