Simple Algebras Base Change And The Advanced Theory Of The Trace Formula
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Simple Algebras Base Change And The Advanced Theory Of The Trace Formula Am 120 Volume 120
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Author : James Arthur
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Simple Algebras Base Change And The Advanced Theory Of The Trace Formula Am 120 Volume 120 written by James Arthur 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.
A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.
Simple Algebras Base Change And The Advanced Theory Of The Trace Formula
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Author : James Arthur
language : en
Publisher: Princeton, N.J. : Princeton University Press
Release Date : 1989
Simple Algebras Base Change And The Advanced Theory Of The Trace Formula written by James Arthur and has been published by Princeton, N.J. : Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n, E) and GL(n, F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.
Number Theory Trace Formulas And Discrete Groups
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Author : Karl Egil Aubert
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Number Theory Trace Formulas And Discrete Groups written by Karl Egil Aubert and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg Oslo, Norway, July 14-21, 1987 is a collection of papers presented at the 1987 Selberg Symposium, held at the University of Oslo. This symposium contains 30 lectures that cover the significant contribution of Atle Selberg in the field of mathematics. This book is organized into three parts encompassing 29 chapters. The first part presents a brief introduction to the history and developments of the zeta-function. The second part contains lectures on Selberg's considerable research studies on understanding the principles of several aspects of mathematics, including in modular forms, the Riemann zeta function, analytic number theory, sieve methods, discrete groups, and trace formula. The third part is devoted to Selberg's further research works on these topics, with particular emphasis on their practical applications. Some of these research studies, including the integral representations of Einstein series and L-functions; first eigenvalue for congruence groups; the zeta function of a Kleinian group; and the Waring's problem are discussed. This book will prove useful to mathematicians, researchers, and students.
The Selberg Arthur Trace Formula
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Author : Salahoddin Shokranian
language : en
Publisher: Springer
Release Date : 2006-11-14
The Selberg Arthur Trace Formula written by Salahoddin Shokranian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks
Proceedings Of The International Congress Of Mathematicians
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Author : S.D. Chatterji
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Proceedings Of The International Congress Of Mathematicians written by S.D. Chatterji and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes. '...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)
Hilbert Modular Forms With Coefficients In Intersection Homology And Quadratic Base Change
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Author : Jayce Getz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-28
Hilbert Modular Forms With Coefficients In Intersection Homology And Quadratic Base Change written by Jayce Getz 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 2012-03-28 with Mathematics categories.
In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.
Harmonic Analysis The Trace Formula And Shimura Varieties
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Author : Clay Mathematics Institute. Summer School
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Harmonic Analysis The Trace Formula And Shimura Varieties written by Clay Mathematics Institute. Summer School 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 2005 with Harmonic analysis categories.
Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.
Advanced Analytic Number Theory L Functions
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Author : Carlos J. Moreno
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Advanced Analytic Number Theory L Functions written by Carlos J. Moreno 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 2005 with Algebraic number theory categories.
Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.
A Tribute To Emil Grosswald
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Author : Emil Grosswald
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
A Tribute To Emil Grosswald written by Emil Grosswald 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 1993 with Mathematics categories.
Emil Grosswald was a mathematician of great accomplishment and remarkable breadth of vision. This volume pays tribute to the span of his mathematical interests, which is reflected in the wide range of papers collected here. With contributions by leading contemporary researchers in number theory, modular functions, combinatorics, and related analysis, this book will interest graduate students and specialists in these fields. The high quality of the articles and their close connection to current research trends make this volume a must for any mathematics library.
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 Automorphic forms 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