Modern Analysis of Automorphic Forms By Example

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.