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Results in Mathematics

, Volume 29, Issue 1–2, pp 16–41 | Cite as

Kloosterman Sums and their Applications: A Review

  • Norman E. Hurt
Article

Abstract

The article reviews recent work in quantum chaos related to quantum mechanical systems which arise in the study of analytic number theory. The central themes of the review are Kloosterman sums, the Selberg-Kloosterman zeta function, the Kuznecov trace formula, the Sato-Tate distribution, and the appearance of Hecke operators in the study of quantum chaos.

1991 Mathematics Subject Classification

11L05 11F72 11E45 58F20 58F25 

Keywords

Kloosterman sums quantum chaos Selberg trace formula Hecke operators 

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Copyright information

© Birkhäuser Verlag, Basel 1996

Authors and Affiliations

  • Norman E. Hurt
    • 1
  1. 1.Zeta Associates, Inc.FairfaxUSA

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