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Modern Analysis of Automorphic Forms By Example (Cambridge Studies in Advanced Mathematics, Series Number 173) (Volume 1)

Modern Analysis of Automorphic Forms By Example (Cambridge Studies in Advanced Mathematics, Series Number 173) (Volume 1)

Modern Analysis of Automorphic Forms By Example (Cambridge Studies in Advanced
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Modern Analysis of Automorphic Forms By Example (Cambridge Studies in Advanced Mathematics, Series Number 173) (Volume 1) Hardback - 2018

by Garrett, Paul

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From the publisher

This is Volume 1 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. 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.

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