An Introduction To Automorphic Representations

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An Introduction To Automorphic Representations

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Author : Jayce R. Getz
language : en
Publisher: Springer Nature
Release Date :

An Introduction To Automorphic Representations written by Jayce R. Getz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Smooth Automorphic Forms And Smooth Automorphic Representations

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Author : Harald Grobner
language : en
Publisher: World Scientific
Release Date : 2023-06-09

Smooth Automorphic Forms And Smooth Automorphic Representations written by Harald Grobner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-09 with Mathematics categories.

This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.Our approach to automorphic representations differs from the usual literature: We do not consider 'K-finite' automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of 'smooth-automorphic forms' is intrinsic to the group scheme G/F.This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G.Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail.

Automorphic Forms On Gl 3 Tr

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Author : D. Bump
language : en
Publisher: Springer
Release Date : 2006-12-08

Automorphic Forms On Gl 3 Tr written by D. Bump and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

Automorphic Representations L Functions And Applications Progress And Prospects

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Author : James W. Cogdell
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

Automorphic Representations L Functions And Applications Progress And Prospects written by James W. Cogdell and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.

This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representations (Gan–Gurevich, Ginzburg–Rallis–Soudry) representation theory of p-adic groups (Baruch, Kudla–Rallis, Mœglin, Cogdell–Piatetski-Shapiro–Shahidi) p-adic methods (Harris–Li–Skinner, Vigneras), and arithmetic applications (Chinta–Friedberg–Hoffstein). The survey articles by Bump, on the Rankin–Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.

Automorphic Representations Of Unitary Groups In Three Variables

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Author : Jonathan David Rogawski
language : en
Publisher: Princeton University Press
Release Date : 1990-09-21

Automorphic Representations Of Unitary Groups In Three Variables written by Jonathan David Rogawski and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-09-21 with Mathematics categories.

The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.

Automorphic Representation Of Unitary Groups In Three Variables Am 123 Volume 123

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Author : Jonathan David Rogawski
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Automorphic Representation Of Unitary Groups In Three Variables Am 123 Volume 123 written by Jonathan David Rogawski and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.

The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.

An Introduction To The Langlands Program

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Author : Joseph Bernstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11

An Introduction To The Langlands Program written by Joseph Bernstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.

Automorphic Forms And Shimura Varieties Of Pgsp 2

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Author : Yuval Z. Flicker
language : en
Publisher: World Scientific
Release Date : 2005

Automorphic Forms And Shimura Varieties Of Pgsp 2 written by Yuval Z. Flicker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftings.OCO This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to LanglandsOCO program in the area of automorphic representations. It includes a proof of known cases of ArtinOCOs conjecture."

Arthur S Invariant Trace Formula And Comparison Of Inner Forms

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Author : Yuval Z. Flicker
language : en
Publisher: Birkhäuser
Release Date : 2016-09-14

Arthur S Invariant Trace Formula And Comparison Of Inner Forms written by Yuval Z. Flicker and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-14 with Mathematics categories.

This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations. It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details. The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner forms in general. Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula. The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G and for functions with matching orbital integrals.bribr/i/idiviiArthur’s Invariant Trace Formula and Comparison of Inner Forms/div

Automorphic Forms Representations And L Functions

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Author : Armand Borel
language : en
Publisher: American Mathematical Soc.
Release Date : 1979-06-30

Automorphic Forms Representations And L Functions written by Armand Borel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-06-30 with Mathematics categories.

Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions