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Eigenfunctions of transfer operators and automorphic forms for Hecke triangel groups of infinite covolume /

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Bibliographic Details
Main Authors: Bruggeman, Roelof W., 1944- (Author), Pohl, Anke (Author)
Format: Electronic eBook
Language:English
Published: Providence, RI : American Mathematical Society, 2023.
Subjects:
Automorphic functions.
Number theory.
Spectral theory (Mathematics)
Online Access: Full text (MFA users only)
ISBN:9781470475390
1470475391
Local Note:ProQuest Ebook Central
Table of Contents:
  • Cover
  • Title page
  • Chapter 1. Introduction
  • Motivational background
  • Aim of this monograph
  • Acknowledgement
  • Part 1. Preliminaries, properties of period functions, and some insights
  • Chapter 2. Notations
  • Chapter 3. Elements from hyperbolic geometry
  • 3.1. Models and isometries
  • 3.2. Classification of isometries
  • 3.3. Cusps, funnels, limit set, and ordinary points
  • 3.4. Geodesics, resonances, and the Selberg zeta function
  • 3.5. Intervals and rounded neighborhoods
  • Chapter 4. Hecke triangle groups with infinite covolume
  • Chapter 5. Automorphic forms
  • 5.1. Funnel forms of different types
  • 5.2. Fourier expansion
  • Chapter 6. Principal series
  • 6.1. Regularity at infinity
  • 6.2. Presheaves and sheaves
  • 6.3. Holomorphic extensions
  • Chapter 7. Transfer operators and period functions
  • 7.1. Discretizations and transfer operators
  • 7.2. Slow transfer operators
  • 7.3. Period functions
  • 7.4. Real and complex period functions
  • 7.5. Fast transfer operators
  • 7.6. One-sided averages
  • 7.7. Convergence and meromorphic extension of fast transfer operators
  • 7.8. Spaces of complex period functions
  • Chapter 8. An intuition and some insights
  • Part 2. Semi-analytic cohomology
  • Chapter 9. Abstract cohomology spaces
  • 9.1. Standard group cohomology
  • 9.2. Cohomology on an invariant set
  • 9.3. Relation to parabolic cohomology spaces
  • Chapter 10. Modules
  • 10.1. Modules of semi-analytic functions
  • 10.2. Submodules of semi-analytic vectors
  • 10.3. Conditions on cocycles
  • 10.4. Cohomological interpretation of the singularity condition
  • Part 3. Automorphic forms and cohomology
  • Chapter 11. Invariant eigenfunctions via a group cohomology
  • Chapter 12. Tesselation cohomology
  • 12.1. Choice of a tesselation, and cohomology
  • 12.2. Relation to group cohomology
  • 12.3. Mixed cohomology spaces
  • Chapter 13. Extension of cocycles
  • Chapter 14. Surjectivity I: Boundary germs
  • 14.1. Analytic boundary germs and semi-analytic modules
  • 14.2. Cohomology classes attached to funnel forms
  • 14.3. Representatives of boundary germs
  • Chapter 15. Surjectivity II: From cocycles to funnel forms
  • 15.1. From a cocycle to an invariant eigenfunction
  • 15.2. A cocycle on an orbit of ordinary points
  • 15.3. Isomorphisms
  • Chapter 16. Relation between cohomology spaces
  • Chapter 17. Proof of Theorem D
  • From funnel forms to cocycle classes on the invariant set
  • From cocycle classes on to funnel forms
  • Proof of Theorem D
  • Part 4. Transfer operators and cohomology
  • Chapter 18. The map from functions to cocycles
  • Chapter 19. Real period functions and semi-analytic cocycles
  • Chapter 20. Complex period functions and semi-analytic cohomology
  • Chapter 21. Proof of Theorem E
  • Part 5. Proofs of Theorems A and B, and a recapitulation
  • Part 6. Parity
  • Chapter 22. The triangle group in the projective general linear group
  • 22.1. Two actions of the projective general linear group

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