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Author: Paul Garrett
Publisher: Cambridge University Press
Published: 2018-09-20
Total Pages: 367
ISBN-13: 1108473849
DOWNLOAD EBOOKVolume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
Author: Paul Garrett
Publisher: Cambridge University Press
Published: 2018-09-20
Total Pages: 407
ISBN-13: 1108228240
DOWNLOAD EBOOKThis 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.
Author: Paul Garrett
Publisher: Cambridge University Press
Published: 2018-09-20
Total Pages: 0
ISBN-13: 9781107154001
DOWNLOAD EBOOKThis 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.
Author: Paul Garrett
Publisher: Cambridge University Press
Published: 2018-09-20
Total Pages: 407
ISBN-13: 1107154006
DOWNLOAD EBOOKVolume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
Author: Paul Garrett
Publisher: Cambridge University Press
Published: 2018-09-20
Total Pages: 367
ISBN-13: 1108669212
DOWNLOAD EBOOKThis is Volume 2 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 2 features critical results, which are proven carefully and in detail, including automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. Volume 1 features discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. 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.
Author: Roelof W. Bruggeman
Publisher: Birkhäuser
Published: 1994-07
Total Pages: 336
ISBN-13:
DOWNLOAD EBOOKThis text gives a systematic treatment of real analytic automorphic forms on the upper half plane for general confinite discrete subgroups. It introduces the main ideas then offers many examples that clarify the general theory and results developed therefrom.
Author: Armand Borel
Publisher: Cambridge University Press
Published: 1997-08-28
Total Pages: 204
ISBN-13: 1316582639
DOWNLOAD EBOOKThis 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 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.
Author: Anton Deitmar
Publisher: Springer Science & Business Media
Published: 2012-08-29
Total Pages: 255
ISBN-13: 144714435X
DOWNLOAD EBOOKAutomorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Author: Jan Hendrik Bruinier
Publisher: Springer
Published: 2018-02-22
Total Pages: 367
ISBN-13: 3319697129
DOWNLOAD EBOOKThis book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.
Author: Stephen S. Gelbart
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 227
ISBN-13: 1400881617
DOWNLOAD EBOOKThis volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?
