Index

analytic vectors in principal series 4

antisymmetrization 26

attracting fixed point 15

augmentation 22

augmentation ideal 30

average 15, 33

base point 23

bilinear Petersson product 117

boundary germ 11

boundary jet 14

boundary map 22

boundary of hyperbolic plane 2

cap product 29

1-chain 26

chain complex on H 25

circle model of principal series 5

coboundary 22

cochain 22

cocompact 25

cocycle relation 29

cofinite 61

cohomology group 21, 28

coinvariants 22

commutator subgroup 84

cup product 117

cup product for parabolic cohomology

119

cusp 61

cusp form 62

1-cycle 26

cyclic interval 18

Dirichlet fundamental domain 28, 65

disk model of hyperbolic plane 1

distribution vectors in principal series 7

duality 7, 13

edge 26

λs-eigenfunction 1

Eisenstein series 92

excised neighborhood 51

extended upper half-plane 65

Fourier expansion 39

free-space resolvent kernel 3

fundamental class 28, 70, 118

fundamental domain 27, 65

geodesic 1

Green’s form viii, 3

group ring 30

homogeneous cocycle 22

homology group 21

horocycle 65

horocyclic disk 65

hyperbolic distance 2

hyperbolic element 15

hyperbolic fixed point 15

hyperbolic plane 1

hyperfunction 6

inhomogeneous cocycle 22

intertwining operator 8

invariant eigenfunction ix, 62

invariants 15

isometry group 2

Laplace operator 2

line model of principal series 4

locally defined module 80

Maass cusp form viii, ix, 62

Maass form viii, ix, 62

Maass-Selberg relation 91

mixed parabolic cocycle 63

mixed parabolic cohomology group x, 63,

69

modular group viii, x, 62, 84

one-sided average 15

parabolic cocycle 63

parabolic cohomology group x, 63, 68

parabolic element 18

parabolic fixed point 18

parabolic resolution 68

period function x, 85, 112

periodlike function 85

129