Smooth Automorphic Forms And Smooth Automorphic Representations

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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 Automorphic Representations And Arithmetic

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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Automorphic Forms Automorphic Representations And Arithmetic written by Robert S. Doran 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 1999 with categories.

Representation Theory And Automorphic Forms

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Author : T. N. Bailey
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Representation Theory And Automorphic Forms written by T. N. Bailey 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 1997 with Mathematics categories.

The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR

An Introduction To Automorphic Representations

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Author : Jayce R. Getz
language : en
Publisher: Springer Nature
Release Date : 2024-03-01

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 2024-03-01 with Mathematics categories.

The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research. The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics. The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields. The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise. Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings. This preparation complete, the global Langlands functoriality conjectures are stated and known cases are discussed. This is followed by a treatment of distinguished representations in global and local settings. The link between distinguished representations and geometry is explained in a chapter on the cohomology of locally symmetric spaces (in particular, Shimura varieties). The trace formula, an immensely powerful tool in the Langlands Program, is discussed in the final chapters of the book. Simple versions of the general relative trace formulae are treated for the first time in a textbook, and a wealth of related material on algebraic group actions is included. Outlines for several possible courses are provided in the Preface.

Lectures On Automorphic L Functions

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Author : James W. Cogdell
language : en
Publisher: American Mathematical Soc.
Release Date :

Lectures On Automorphic L Functions written by James W. Cogdell 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 with Mathematics categories.

James W. Cogdell, Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$: Preface Modular forms and their $L$-functions Automorphic forms Automorphic representations Fourier expansions and multiplicity one theorems Eulerian integral representations Local $L$-functions: The non-Archimedean case The unramified calculation Local $L$-functions: The Archimedean case Global $L$-functions Converse theorems Functoriality Functoriality for the classical groups Functoriality for the classical groups, II Henry H. Kim, Automorphic $L$-functions: Introduction Chevalley groups and their properties Cuspidal representations $L$-groups and automorphic $L$-functions Induced representations Eisenstein series and constant terms $L$-functions in the constant terms Meromorphic continuation of $L$-functions Generic representations and their Whittaker models Local coefficients and non-constant terms Local Langlands correspondence Local $L$-functions and functional equations Normalization of intertwining operators Holomorphy and bounded in vertical strips Langlands functoriality conjecture Converse theorem of Cogdell and Piatetski-Shapiro Functoriality of the symmetric cube Functoriality of the symmetric fourth Bibliography M. Ram Murty, Applications of symmetric power $L$-functions: Preface The Sato-Tate conjecture Maass wave forms The Rankin-Selberg method Oscillations of Fourier coefficients of cusp forms Poincare series Kloosterman sums and Selberg's conjecture Refined estimates for Fourier coefficients of cusp forms Twisting and averaging of $L$-series The Kim-Sarnak theorem Introduction to Artin $L$-functions Zeros and poles of Artin $L$-functions The Langlands-Tunnell theorem Bibliography

The Descent Map From Automorphic Representations Of Gl N To Classical Groups

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Author : David Ginzburg
language : en
Publisher: World Scientific
Release Date : 2011

The Descent Map From Automorphic Representations Of Gl N To Classical Groups written by David Ginzburg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

1. Introduction. 1.1. Overview. 1.2. Formulas for the Weil representation. 1.3. The case, where H is unitary and the place v splits in E -- 2. On certain residual representations. 2.1. The groups. 2.2. The Eisenstein series to be considered. 2.3. L-groups and representations related to P[symbol]. 2.4. The residue representation. 2.5. The case of a maximal parabolic subgroup (r = 1). 2.6. A preliminary lemma on Eisenstein series on GL[symbol]. 2.7. Constant terms of E(h, f[symbol]). 2.8. Description of W(M[symbol], D[symbol]). 2.9. Continuation of the proff of Theorem 2.1 -- 3. Coefficients of Gelfand-Graev type, of Fourier-Jacobi type, and descent. 3.1. Gelfand-Graev coefficients. 3.2. Fourier-Jacobi coefficients. 3.3. Nilpotent orbits. 3.4. Global integrals representing L-functions I. 3.5. Global integrals representing L-functions II. 3.6. Definition of the descent. 3.7. Definition of Jacquet modules corresponding to Gelfand-Graev characters. 3.8. Definition of Jacquet modules corresponding to Fourier-Jacobi characters -- 4. Some double coset decompositions. 4.1. The space Q[symbol]. 4.2. A set of representatives for Q[symbol]. 4.3. Stabilizers. 4.4. The set Q\h[symbol] -- 5. Jacquet modules of parabolic inductions : Gelfand-Graev characters. 5.1. The case where K is a field. 5.2. The case K = k[symbol]k -- 6. Jacquet modules of parabolic inductions : Fourier-Jacobi characters. 6.1. The case where K is a field. 6.2. The case K = k[symbol]k -- 7. The tower property. 7.1. A general lemma on "exchanging roots". 7.2. A formula for constant terms of Gelfand-Graev coefficients. 7.3. Global Gelfand-Graev models for cuspidal representations. 7.4. The general case : H is neither split nor quasi-split. 7.5. Global Gelfand-Graev models for the residual representations E[symbol]. 7.6. A formula for constant terms of Fourier-Jacobi coefficients. 7.7. Global Fourier-Jacobi models for cuspidal representations. 7.8. Global Fourier-Jacobi models for the residual representations E[symbol]

Automorphic Forms And Related Geometry Assessing The Legacy Of I I Piatetski Shapiro

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Author : James W. Cogdell
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-01

Automorphic Forms And Related Geometry Assessing The Legacy Of I I Piatetski Shapiro written by James W. Cogdell 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 2014-04-01 with Mathematics categories.

This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.

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

Automorphic Forms And Representations

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Author : Daniel Bump
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-28

Automorphic Forms And Representations written by Daniel Bump and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-28 with Mathematics categories.

This book takes advanced graduate students from the foundations to topics on the research frontier.

Automorphic Forms And L Functions I

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Author : David Ginzburg
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Automorphic Forms And L Functions I written by David Ginzburg 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 2009 with Mathematics categories.

Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.