Automorphic Forms on SL2 (R)Cambridge University Press, 1997 M08 28 - 192 páginas This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup ^D*G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on ^D*G\G and its relationship with the classical automorphic forms on X, Poincaré series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2(^D*G/G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. |
Contenido
Automorphic forms and cusp forms | 53 |
Poincaré series | 69 |
given type | 75 |
Convolution operators on cuspidal functions | 81 |
Eisenstein series | 87 |
11 | 93 |
Analytic continuation of the Eisenstein series | 99 |
Eisenstein series and automorphic forms orthogonal to cusp forms | 119 |
Spectral decomposition and representations | 145 |
the continuous spectrum | 171 |
| 185 | |
Otras ediciones - Ver todas
Términos y frases comunes
analytic continuation assertion Assume automorphic form bounded Cartan subgroup Casimir operator compact set compact subset constant term contains converges convolution cusp forms cuspidal parabolic subgroup cuspidal point defined definition denote differential operators Dirac sequence direct sum disc eigenvalue Eisenstein series element equivalent exists a constant finite dimensional follows function f function on G fundamental domain geodesic given Haar measure hence holomorphic horodisc implies invariant irreducible isomorphism K-finite left-hand side left-invariant Lemma Let f Lie algebra linear Maass-Selberg relations meromorphic functions moderate growth neighborhood nonzero notation orthogonal p-pair parabolic subgroup Poincaré series pole of order polynomial principal series Proof prove quotient relatively compact representations of G resp right K-type right-hand side scalar product Section self-adjoint Si,t Siegel set space spanned square integrable theorem transform vector write zero