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Selberg trace formulae and equidistribution theorems for closed geodesics and Laplace eigenfunctions: finite area surfaces

About this Title

Steven Zelditch

Publication: Memoirs of the American Mathematical Society
Publication Year: 1992; Volume 96, Number 465
ISBNs: 978-0-8218-2526-6 (print); 978-1-4704-0891-6 (online)
DOI: https://doi.org/10.1090/memo/0465
MathSciNet review: 1101972
MSC: Primary 11F72; Secondary 58G25

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Table of Contents

Chapters

  • 0. Introduction
  • 1. Review of [Z.2] on the compact case
  • 2. Trace formula for $\operatorname {Tr} \sigma R^\Gamma _\varphi$ ($\sigma$ cuspidal)
  • 3. Trace formula for $\operatorname {Tr} \sigma R^\Gamma _\varphi$ ($\sigma$ Eisenstein)
  • 4. Spectral estimates (Weyl laws)
  • 5. Asymptotic expansions (prime geodesic theorems)
  • 6. Equidistribution of closed geodesies
  • Appendix