Modern analysis of automorphic forms by example.
Garrett, Paul B.,
Modern analysis of automorphic forms by example. Volume 1 / Paul Garrett. - Cambridge : Cambridge University Press, 2018. - 1 online resource (xxii, 384 pages) : digital, PDF file(s). - Cambridge studies in advanced mathematics ; 173 . - Cambridge studies in advanced mathematics ; 173. .
Title from publisher's bibliographic system (viewed on 14 Sep 2018).
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.
9781316650332 (ebook)
Automorphic forms.
Forms (Mathematics)
QA353.A9 / G37 2018
515/.9
Modern analysis of automorphic forms by example. Volume 1 / Paul Garrett. - Cambridge : Cambridge University Press, 2018. - 1 online resource (xxii, 384 pages) : digital, PDF file(s). - Cambridge studies in advanced mathematics ; 173 . - Cambridge studies in advanced mathematics ; 173. .
Title from publisher's bibliographic system (viewed on 14 Sep 2018).
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.
9781316650332 (ebook)
Automorphic forms.
Forms (Mathematics)
QA353.A9 / G37 2018
515/.9