Automorphic Forms

2.1 Groups Kv = GL2(ov ) ⊂ Gv = GL2(kv ) 56

2.2 Discrete Subgroup GL2(k) ⊂ GL2(A), Reduction Theory 59

2.3 Invariant Measures 67

2.4 Hecke Operators, Integral Operators 70

2.5 Decomposition by Central Characters 74

2.6 Discrete Decomposition of Cuspforms 76

2.7 Pseudo-Eisenstein Series 79

2.8 Eisenstein Series 85

2.9 Meromorphic Continuation of Eisenstein Series 96

2.10 Truncation and Maaß-Selberg Relations 100

2.11 Decomposition of Pseudo-Eisenstein Series: Level One 105

2.12 Decomposition of Pseudo-Eisenstein Series: Higher Level 114

2.13 Plancherel for Pseudo-Eisenstein Series: Level One 119

2.14 Spectral Expansion, Plancherel Theorem: Level One 124

2.15 Exotic Eigenfunctions, Discreteness of Pseudo-Cuspforms 126

References

Paul Garrett, Modern Analysis of Automorphic Forms by Example.