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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.
| Autorius: | Armand Borel |
| Leidėjas: | Cambridge University Press |
| Išleidimo metai: | 2004 |
| Knygos puslapių skaičius: | 208 |
| ISBN-10: | 0521580498 |
| ISBN-13: | 9780521580496 |
| Formatas: | 235 x 157 x 17 mm. Knyga kietu viršeliu |
| Kalba: | Anglų |
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