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Regular $b$-groups, degenerating Riemann surfaces, and spectral theory

About this Title

Dennis A. Hejhal

Publication: Memoirs of the American Mathematical Society
Publication Year: 1990; Volume 88, Number 437
ISBNs: 978-0-8218-2499-3 (print); 978-1-4704-0860-2 (online)
DOI: https://doi.org/10.1090/memo/0437
MathSciNet review: 1052555
MSC: Primary 11F72; Secondary 14H15, 32G15, 58G25

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Table of Contents

Chapters

  • Introduction
  • 1. Riemann surfaces with nodes and regular b-groups
  • 2. The space $\mathcal {M}_g$
  • 3. Convergence of Green’s functions (part one)
  • 4. Collars and nodal neighborhoods
  • 5. An apriori bound for prime geodesics
  • 6. Convergence of Green’s functions (part two)
  • 7. Continuity properties of small eigenvalues
  • 8. Asymptotic properties of the Selberg zeta function
  • 9. An analog of Weyl’s law