Book Description
An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.
Author : Armand Borel
Publisher : Cambridge University Press
Page : 226 pages
File Size : 20,47 MB
Release : 1997-08-28
Category : Mathematics
ISBN : 9780521580496
An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.
Author : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 31,64 MB
Release : 2012-08-29
Category : Mathematics
ISBN : 144714435X
Automorphic 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 : Armand Borel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 13,94 MB
Release : 1979-06-30
Category : Mathematics
ISBN : 0821814370
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Author : D. Bump
Publisher : Springer
Page : 196 pages
File Size : 28,32 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540390553
Author : H. Jacquet
Publisher : Springer
Page : 156 pages
File Size : 47,16 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540376127
Author : Paul Garrett
Publisher : Cambridge University Press
Page : 407 pages
File Size : 30,28 MB
Release : 2018-09-20
Category : Mathematics
ISBN : 1107154006
Volume 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
Page : 407 pages
File Size : 10,61 MB
Release : 2018-09-20
Category : Mathematics
ISBN : 1107154006
Volume 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
Page : 367 pages
File Size : 23,24 MB
Release : 2018-09-20
Category : Mathematics
ISBN : 1108669212
This 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 : Terry Gannon
Publisher : Cambridge University Press
Page : 493 pages
File Size : 29,97 MB
Release : 2023-07-31
Category : Science
ISBN : 1009401580
Author : Yuval Zvi Flicker
Publisher : World Scientific
Page : 499 pages
File Size : 45,66 MB
Release : 2006
Category : Mathematics
ISBN : 9812773622
The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftingsOCO. This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E: F] = 2. The book develops the technique of comparison of twisted and stabilized trace formulae and considers the OC Fundamental LemmaOCO on orbital integrals of spherical functions. Comparison of trace formulae is simplified using OC regularOCO functions and the OC liftingOCO is stated and proved by means of character relations. This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent. There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne''s (proven) conjecture on the fixed point formula. Sample Chapter(s). Chapter 1: Functoriality and Norms (963 KB). Contents: On the Symmetric Square Lifting: Functoriality and Norms; Orbital Integrals; Twisted Trace Formula; Total Global Comparison; Applications of a Trace Formula; Computation of a Twisted Character; Automorphic Representations of the Unitary Group U(3, E/F): Local Theory; Trace Formula; Liftings and Packets; Zeta Functions of Shimura Varieties of U(3): Automorphic Representations; Local Terms; Real Representations; Galois Representations. Readership: Graduate students and researchers in number theory, algebra and representation theory."