Arthur, James 1944
Overview
Works:  20 works in 105 publications in 3 languages and 1,719 library holdings 

Genres:  Conference papers and proceedings Directories 
Roles:  Author, Editor 
Classifications:  QA171, 512.2 
Publication Timeline
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Most widely held works about
James Arthur
 Arthur's trace formula for SO(5) and individual discrete series matix coefficients by Stephen Thomas Spallone( )
 Arthur, James Greig : Automorphic Forms, Group Representations( )
Most widely held works by
James Arthur
Simple algebras, base change, and the advanced theory of the trace formula by
James Arthur(
Book
)
15 editions published between 1988 and 2016 in English and Undetermined and held by 403 WorldCat member libraries worldwide
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
15 editions published between 1988 and 2016 in English and Undetermined and held by 403 WorldCat member libraries worldwide
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
The SelbergArthur trace formula : based on lectures by James Arthur by
Salahoddin Shokranian(
Book
)
15 editions published between 1991 and 1992 in English and German and held by 322 WorldCat member libraries worldwide
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 noncommutative 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 Ifunction, 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
15 editions published between 1991 and 1992 in English and German and held by 322 WorldCat member libraries worldwide
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 noncommutative 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 Ifunction, 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
The endoscopic classification of representations orthogonal and symplectic groups by
James Arthur(
Book
)
9 editions published in 2013 in English and held by 217 WorldCat member libraries worldwide
9 editions published in 2013 in English and held by 217 WorldCat member libraries worldwide
Representation theory of real reductive Lie groups : AMSIMSSIAM Joint Summer Research Conference, June 48, 2006, Snowbird,
Utah by AMSIMSSIAM Joint Summer Research Conference(
Book
)
12 editions published in 2008 in English and held by 188 WorldCat member libraries worldwide
"The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at The AMSIMSSIAM Joint Summer Research Conference "Representation Theory of Real Reductive Lie Groups" held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature." "This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields."Jacket
12 editions published in 2008 in English and held by 188 WorldCat member libraries worldwide
"The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at The AMSIMSSIAM Joint Summer Research Conference "Representation Theory of Real Reductive Lie Groups" held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature." "This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields."Jacket
Harmonic analysis, the trace formula, and Shimura varieties : proceedings of the Clay Mathematics Institute, 2003 Summer School,
the Fields Institute, Toronto, Canada, June 227, 2003 by
Clay Mathematics Institute(
Book
)
8 editions published in 2005 in English and held by 170 WorldCat member libraries worldwide
8 editions published in 2005 in English and held by 170 WorldCat member libraries worldwide
On certain Lfunctions : conference in honor of Freydoon Shahidi on certain Lfunctions, Purdue University, West Lafayette,
Indiana, July 2327, 2007 by Conference on Certain LFunctions(
Book
)
9 editions published in 2011 in English and held by 93 WorldCat member libraries worldwide
9 editions published in 2011 in English and held by 93 WorldCat member libraries worldwide
A local trace formula by
James Arthur(
Book
)
5 editions published between 1989 and 1991 in English and French and held by 18 WorldCat member libraries worldwide
5 editions published between 1989 and 1991 in English and French and held by 18 WorldCat member libraries worldwide
Citizenship education(
Book
)
6 editions published in 2008 in English and held by 11 WorldCat member libraries worldwide
6 editions published in 2008 in English and held by 11 WorldCat member libraries worldwide
Journées automorphes by
James Arthur(
Book
)
7 editions published in 1983 in 3 languages and held by 8 WorldCat member libraries worldwide
7 editions published in 1983 in 3 languages and held by 8 WorldCat member libraries worldwide
The eucharistic dialogue after Vatican II from catholic and ecumenical perspective by
James Arthur(
Book
)
5 editions published in 1992 in English and held by 7 WorldCat member libraries worldwide
5 editions published in 1992 in English and held by 7 WorldCat member libraries worldwide
Harmonic analysis of tempered distributions on semisimple lie groups of real rank one by
James G Arthur(
Book
)
3 editions published in 1970 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1970 in English and held by 3 WorldCat member libraries worldwide
Representations of real reductive Lie groups : AMSIMSSIAM Joint Summer Research Conference [on Representation Theory of
Real Reductive Lie Groups], June 48, 2006, Snowbird, Utah by AMSIMSSIAM Joint Summer Research Conference(
Book
)
3 editions published in 2008 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2008 in English and held by 3 WorldCat member libraries worldwide
The Fourier transform of weighted orbital integrals on SL(2,R) by
James Arthur(
Book
)
1 edition published in 1985 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 2 WorldCat member libraries worldwide
The collected works of James G. Arthur by
James Arthur(
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
Harmonic analysis of tempered distributiohs on semisimple Lie groups of real rank one, dissertation by
James Arthur(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
World directory of mathematicians, 1998 by
International Mathematical Union(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
Unipotent automorphic representations : conjectures by
James Arthur(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
Simple Algebras by
James Arthur(
)
1 edition published in 1989 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Clozel, Laurent 1953 Contributor
 Shokranian, Salahoddin 1948 Author
 Schmid, Wilfried 1943 Editor
 Trapa, Peter E. 1974 Editor
 Ellwood, David 1966 Editor
 Kottwitz, Robert E. Editor
 Clay Mathematics Institute Summer School (2003 : Toronto, Ont.)
 Shahidi, Freydoon Dedicatee
 SpringerLink (Service en ligne)
 Institut des hautes études scientifiques (Paris, France)
Useful Links
Associated Subjects
Algebraic number theory Arthur, James, Automorphic forms Automorphisms Awards BaptismCatholic Church Canada CitizenshipStudy and teaching Class field theory College teachers Executives Galois theory Geometry, Algebraic Group theory Harmonic analysis Lfunctions Lie groups Linear algebraic groups Lord's SupperCatholic Church Mathematicians Mathematics Number theory Representations of groups Representations of Lie groups Research Riemann surfaces SacramentsCatholic Church Scientists Selberg trace formula Shimura varieties Teachers Topological groups Trace formulas United States
Alternative Names
Arthur, J. 1944
Arthur, J. (James), 1944
Arthur, James Greig 1944
James Arthur Canadees wiskundige
James Arthur Canadian mathematician
James Arthur canadisk matematiker
James Arthur kanadensisk matematiker
James Arthur kanadischer Mathematiker
James Arthur kanadisk matematikar
James Arthur kanadisk matematiker
Джеймс Артур канадский математик
ג'יימס ג. ארתור
جيمس آرثر (رياضياتي)
جیمز آرتور ریاضیدان کانادایی
詹姆斯·亚瑟
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