The collected works of James G. Arthur

Photo: Bill Casselman

James Arthur was born on May 18, 1944. He attended the University of Toronto as an undergraduate, and received his Ph. D. at Yale University in 1970, where his advisor was Robert Langlands. He has been a University Professor at the University of Toronto since 1987.

The papers (arranged by topic)

Unrefined trace formula and truncation

Invariant trace formula and refined expansions

Stable trace formula and endoscopy

Characters, Hecke operators, L²-cohomology

Some tempered distributions on semisimple groups of real rank one (1974)

The characters of discrete series as orbital integrals (1976)

The characters of supercuspidal representations as weighted orbital integrals (1987)

Characters, harmonic analysis, and an L²-Lefschetz formula (1988)

The trace formula and Hecke operators (1989)

The L²-Lefschetz numbers of Hecke operators (1989)

L²-cohomology and automorphic representations (1996)

On local character relations (1996)

Intertwining operators

Intertwining operators and residues I. Weighted characters (1989)

Intertwining operators and residues II. Invariant distributions (1989)

Canonical normalization of weighted characters and a transfer conjecture (1998)

Induced representations, intertwining operators, and transfer for real groups (2008)

Harmonic analysis and nonabelian Fourier transforms

A theorem on the Schwartz space of a reductive Lie group (1975)

Harmonic analysis of invariant distributions (1978)

A Paley-Wiener theorem for real reductive groups (1983)

Multipliers and a Paley-Wiener theorem for real reductive groups (1983)

The Fourier transform of weighted orbital integrals on SL(2,R) (1986)

Harmonic analysis of tempered distributions on semisimple Lie groups of real rank one (1989)

The trace Paley Wiener theorem for Schwartz functions (1994)

Germ expansions for real groups (2004)

An asymptotic formula for real groups (2006)

Problems for real groups (2008)

Local trace formula and applications

Towards a local trace formula (1989)

Some problems in local harmonic analysis (1991)

A local trace formula (1991)

On the Fourier transforms of weighted orbital integrals (1994)

Functoriality and classification of representations

On some problems suggested by the trace formula (1984)

Unipotent automorphic representations: conjectures (1989)

Unipotent automorphic representations: global motivation (1990)

On elliptic tempered characters (1993)

The problem of classifying automorphic representations of classical groups (1997)

A note on the automorphic Langlands group (2002)

The principle of functoriality (2003)

Automorphic representations of GSp(4) (2004)

A note on L-packets (2006)

The embedded eigenvalue problem for classical groups (2008)

Monographs

Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula (1989)

The Endoscopic Classification of Representations: Orthogonal and Symplectic Groups. Published in 2013 as volume 61 in the series of Colloquium Publications by the American Mathematical Society.

General exposition

Automorphic representations and number theory (1981)

Lectures on automorphic L-functions (1991)

Harmonic analysis and group representations (2000)

An introduction to the Trace Formula (2005)

Report on the trace formula (2009)

Miscellaneous

Armand Borel (1923--2003) (2004)

Harmonic analysis in mathematics (2005)

AMS President's address at Abel celebration (2005)

A (very brief) history of the trace formula (2007)

Transfer, the Fundamental Lemma, and the work of Waldspurger (2009)

The work of Ngô Bau Châu (2010)