Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120
Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120

Author: James Arthur

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 248

ISBN-13: 1400882400

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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
Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula

Author: James Arthur

Publisher: Princeton, N.J. : Princeton University Press

Published: 1989

Total Pages: 230

ISBN-13: 9780691085173

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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.

Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures
Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures

Author: Rajendra Bhatia

Publisher: World Scientific

Published: 2011-06-06

Total Pages: 4137

ISBN-13: 9814462934

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ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Operator Algebras, Operator Theory and Applications
Operator Algebras, Operator Theory and Applications

Author: Maria Amélia Bastos

Publisher: Springer Science & Business Media

Published: 2008-05-27

Total Pages: 443

ISBN-13: 3764386843

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This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The book is aimed at postgraduates and researchers in these fields.

C*-algebras and Elliptic Theory II
C*-algebras and Elliptic Theory II

Author: Dan Burghelea

Publisher: Springer Science & Business Media

Published: 2008-03-18

Total Pages: 312

ISBN-13: 3764386045

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This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

Shimura Varieties
Shimura Varieties

Author: Thomas Haines

Publisher: Cambridge University Press

Published: 2020-02-20

Total Pages: 341

ISBN-13: 1108704867

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This volume forms the sequel to "On the stabilization of the trace formula", published by International Press of Boston, Inc., 2011

The Local Langlands Conjecture for GL(2)
The Local Langlands Conjecture for GL(2)

Author: Colin J. Bushnell

Publisher: Springer Science & Business Media

Published: 2006-08-29

Total Pages: 352

ISBN-13: 354031511X

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The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.

Eisenstein Series and Automorphic $L$-Functions
Eisenstein Series and Automorphic $L$-Functions

Author: Freydoon Shahidi

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 218

ISBN-13: 0821849891

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This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.

Proceedings of the Gibbs Symposium
Proceedings of the Gibbs Symposium

Author: D. G. Caldi

Publisher: American Mathematical Soc.

Published: 1990-11-07

Total Pages: 342

ISBN-13: 9780821896716

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This volume, a joint publication with the American Institute of Physics, contains the proceedings of a symposium honoring the memory of Josiah Willard Gibbs, one of the giants of theoretical physics. Three articles provide perspectives on Gibbs, the man, and on the place his work occupies in the history of science. There are also contributions from leading scientists on statistical mechanics, thermodynamics, geophysics, number theory, general relativity, and economics.