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" Modern analysis of automorphic forms by example / "
Paul Garrett (University of Minnesota, Minneapolis, USA).
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BL
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| Record Number
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839094
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| Main Entry
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Garrett, Paul B.
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| Title & Author
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Modern analysis of automorphic forms by example /\ Paul Garrett (University of Minnesota, Minneapolis, USA).
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| Publication Statement
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Cambridge :: Cambridge University Press,, 2018.
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, ©2018
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| Series Statement
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Cambridge studies in advanced mathematics ;; 173-174
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2 volumes ;; 24 cm.
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| ISBN
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1107154006
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: 1108473849
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: 1108697933
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: 9781107154001
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: 9781108473842
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: 9781108697934
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Volume 1. 1. Four small examples ; 2. The quotient Z+GL2(k)/GL2(A) ; 3. SL3(Z), SL5(Z) ; 4. Invariant differential operators ; 5. Integration on quotients ; 6. Action of G on function spaces on G ; 7. Discrete decomposition of cuspforms ; 8. Moderate growth functions, theory of the constant term -- Volume 2. 9. Unbounded operators on Hilbert spaces ; 10. Discrete decomposition of pseudo-cuspforms ; 11. Meromorphic continuation of Eisenstein series ; 12. Global automorphic Sobolev spaces, Green's functions ; 13. Examples -- topologies on natural function spaces ; 14. Vector-valued integrals ; 15. Differentiable vector-valued functions ; 16. Asymptotic expansions.
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| Abstract
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"The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields"--Publisher's description.
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Automorphic forms.
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Forms (Mathematics)
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Analysis
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Automorphe Form
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Automorphic forms.
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Forms (Mathematics)
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| Dewey Classification
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515/.9
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| LC Classification
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QA353.A9G37 2018
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