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Title page

Introduction

Chapter 1. Eigenfunctions of the hyperbolic Laplace operator

1. Eigenfunctions on the hyperbolic plane

2. Principal series

3. Boundary germs and transverse Poisson transform

4. Averages

Chapter 2. Maass forms and analytic cohomology: cocompact groups

5. From Maass forms to analytic cohomology

6. Cohomology for cocompact groups

7. From cohomology to Maass forms

Chapter 3. Cohomology of infinite cyclic subgroups of 𝑃𝑆𝐿₂(ℝ)

8. Invariants

9. Coinvariants

Chapter 4. Maass forms and semi-analytic cohomology: groups with cusps

10. Maass forms

11. Cohomology and parabolic cohomology for groups with cusps

12. Maass forms and cohomology

13. Parabolic cohomology and mixed parabolic cohomology

14. Period functions and periodlike functions for the full modular group

15. Maass forms and holomorphic functions

Chapter 5. Maass forms and differentiable cohomology

16. Differentiable parabolic cohomology

17. Smooth parabolic cohomology

Chapter 6. Distribution cohomology and Petersson product

18. Distribution cohomology

19. Duality

Bibliography

Index

List of notations

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