Euler Products And Eisenstein Series
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Euler Products And Eisenstein Series
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Author : Gorō Shimura
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Euler Products And Eisenstein Series written by Gorō Shimura 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 Eisenstein series categories.
This volume has three chief objectives: 1) the determination of local Euler factors on classical groups in an explicit rational form; 2) Euler products and Eisenstein series on a unitary group of an arbitrary signature; and 3) a class number formula for a totally definite hermitian form. Though these are new results that have never before been published, Shimura starts with a quite general setting. He includes many topics of an expository nature so that the book can be viewed as an introduction to the theory of automorphic forms of several variables, Hecke theory in particular. Eventually, the exposition is specialized to unitary groups, but they are treated as a model case so that the reader can easily formulate the corresponding facts for other groups. There are various facts on algebraic groups and their localizations that are standard but were proved in some old papers or just called well-known. In this book, the reader will find the proofs of many of them, as well as systematic expositions of the topics. This is the first book in which the Hecke theory of a general (nonsplit) classical group is treated. The book is practically self-contained, except that familiarity with algebraic number theory is assumed.
Euler Products And Eisenstein Series
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Author : Gorō Shimura
language : en
Publisher: American Mathematical Soc.
Release Date :
Euler Products And Eisenstein Series written by Gorō Shimura 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.
This volume has three chief objectives: 1) the determination of local Euler factors on classical groups in an explicit rational form; 2) Euler products and Eisenstein sereis on a unitary group of an arbitrary signature; and 3) a class number formula for a totally definite hermitian form. Though these are new results that have never before been published, Shimura starts with a quite general setting. He includes many topics of an expository nature so that the book can be viewed as an introduction to the theory of automorphic forms of several variables, Hecke theory in particular. Eventually, the exposition is specialized to unitary groups, but they are treated as a model case so that the reader can easily formulate the corresponding facts for other groups. There are various facts on algebraic groups and their localiztions that are standard but were proved in some old papers or just called "well-known". In this book, the reader will find the proofs of many of them, as well as systematic expositions of the topics. This is the first book in which the Hecke theory of a general (nonsplit) classical group is treated. The book is practically self-contained, except that familiarity with algebraic number theory is assumed.
Explicit Formulas For Local Factors In The Euler Products For Eisenstein Series
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Author : Mathematical Sciences Research Institute (Berkeley, Calif.).
language : en
Publisher:
Release Date : 1987
Explicit Formulas For Local Factors In The Euler Products For Eisenstein Series written by Mathematical Sciences Research Institute (Berkeley, Calif.). and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
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.
Automorphic Forms Automorphic Representations And Arithmetic
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Author : Robert S. Doran
language : en
Publisher:
Release Date : 1999
Automorphic Forms Automorphic Representations And Arithmetic written by Robert S. Doran and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Automorphic forms categories.
Professor Goro Shimura was principal speaker at the conference on "Euler Products and Eisenstein Series" held at Texas Christian University (See CBMS Regional Conference Series in Mathematics, Volume 93). The present volume contains articles by leading specialists in the field. Some of these articles are based on talks given at the conference, whereas others were written purposely for this volume. The variety of the work presented reflects the current active state of the topic.
Number Theory
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Author : Kazuya Kato
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Number Theory written by Kazuya Kato 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 2000 with Class field theory categories.
Arithmetic And Analytic Theories Of Quadratic Forms And Clifford Groups
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Author : Goro Shimura
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-05-27
Arithmetic And Analytic Theories Of Quadratic Forms And Clifford Groups written by Goro Shimura 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 2014-05-27 with Education categories.
In this book, award-winning author Goro Shimura treats new areas and presents relevant expository material in a clear and readable style. Topics include Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. He also includes some basic results not readily found elsewhere. The two principle themes are: (1) Quadratic Diophantine equations; (2) Euler products and Eisenstein series on orthogonal groups and Clifford groups. The starting point of the first theme is the result of Gauss that the number of primitive representations of an integer as the sum of three squares is essentially the class number of primitive binary quadratic forms. Presented are a generalization of this fact for arbitrary quadratic forms over algebraic number fields and various applications. For the second theme, the author proves the existence of the meromorphic continuation of a Euler product associated with a Hecke eigenform on a Clifford or an orthogonal group. The same is done for an Eisenstein series on such a group. Beyond familiarity with algebraic number theory, the book is mostly self-contained. Several standard facts are stated with references for detailed proofs. Goro Shimura won the 1996 Steele Prize for Lifetime Achievement for "his important and extensive work on arithmetical geometry and automorphic forms".
Lectures
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Author : Erich Hecke
language : en
Publisher:
Release Date : 1938
Lectures written by Erich Hecke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1938 with Dirichlet series categories.
Topics In Classical Automorphic Forms
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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Topics In Classical Automorphic Forms written by Henryk Iwaniec 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.
This volume discusses various perspectives of the theory of automorphic forms drawn from the author's notes from a Rutgers University graduate course. In addition to detailed and often nonstandard treatment of familiar theoretical topics, the author also gives special attention to such subjects as theta- functions and representatives by quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR
Zeros Of Fourier Coefficients Of Metaplectic Eisenstein Series
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Author : David Alan Cardon
language : en
Publisher:
Release Date : 1996
Zeros Of Fourier Coefficients Of Metaplectic Eisenstein Series written by David Alan Cardon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.