| Automorphic Forms on Sl2 (R) Contributor(s): Borel, Armand (Author) |
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ISBN: 0521580498 ISBN-13: 9780521580496 Publisher: Cambridge University Press OUR PRICE: $134.90 Product Type: Hardcover - Other Formats Published: August 1997 Annotation: 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, Poincare 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Calculus |
| Dewey: 515.9 |
| LCCN: 97006027 |
| Series: Cambridge Tracts in Mathematics (Hardcover) |
| Physical Information: 0.63" H x 6" W x 9" (1.05 lbs) 208 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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, Poincar 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. |