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Synopsis
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.
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Book Description
The theory of automorphic forms, which goes back to the work of Poincare and Klein, has been considerably developed and generalized in the last 40 years by the use of new analytic methods, inspired in part by harmonic analysis on Lie groups. This book is devoted to the analytic theory of automorphic forms, limited to the case of fuchsian groups, but from those more general points of view.This first exposition of this approach in this special case should be accessible to researchers and graduate students having some familiarity with functional analysis and elementary Lie theory.
Review
"...is a very carefully written book, which is accessible to the graduate student. ... Its size of 184 pages makes it even more possible to complete the material in one semester. Thus, it can be used as preparation for learning the `Langlands program' since the case of SL2(R) is concrete enough not to be lost in the maze of generality and typical enough to exemplify the general case. The topic is now a dominant theme in both algebraic and analytic number theory as well as algebraic geometry, and so the monograph is timely." Mathematical Reviews Clippings
"...I would recommend [Bu] to graduate students or anyone else who wants to get into the subject. There is a great deal of foundational material here. Any effort put into reading it and working exercises will be rewarded with a good understanding of the basics." Bulletin of the American Mathematical Society
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- PublisherCambridge University Press
- Publication date1997
- ISBN 10 0521580498
- ISBN 13 9780521580496
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages208
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Automorphic Forms on SL2 (R) (Cambridge Tracts in Mathematics, Series Number 130)
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Automorphic Forms on SL2 (R) (Cambridge Tracts in Mathematics, Series Number 130)
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Automorphic Forms on SL2 (R)
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Automorphic Forms on Sl2 (R)
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. An introduction to the analytic theory of automorphic forms, limited to the case of fuchsian groups, but from the point of view of the general theory, ending with an introduction to unitary infinite dimensional representations. The main prerequisites are f. Seller Inventory # 446940875
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Automorphic Forms on Sl2 (R) (Hardcover)
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ISBN 10: 0521580498
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Hardcover. Condition: new. Hardcover. This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2 or the upper-half plane X, with respect to a discrete subgroup 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 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 (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. Graduate students and researchers in analytic number theory will find much to interest them in this book. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521580496
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Automorphic Forms on Sl2 (R)
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ISBN 13: 9780521580496
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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\*GG 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. Seller Inventory # 9780521580496
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Automorphic Forms on SL2 (R) (Cambridge Tracts in Mathematics)
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Automorphic Forms on SL2 (R) (Cambridge Tracts in Mathematics, Series Number 130)
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ISBN 10: 0521580498
ISBN 13: 9780521580496
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Automorphic Forms on Sl2 (R) (Hardcover)
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ISBN 10: 0521580498
ISBN 13: 9780521580496
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Hardcover. Condition: new. Hardcover. This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2 or the upper-half plane X, with respect to a discrete subgroup 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 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 (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. Graduate students and researchers in analytic number theory will find much to interest them in this book. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Seller Inventory # 9780521580496
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