[ Main page on Langlands' work | Copyright notice ]

The work of Robert Langlands


L-indistinguishability for SL(2) (written with J.-P. Labesse)

This first appeared in the Can. Jour. Math. 31 (1979).

Stable conjugacy-definitions and lemmas

This first appeared in Can. J. Math. XXXI (1979).

Les débuts d'une formule des traces stable

This originally appeared as a monograph published by the University of Paris VII.

Langlands' comments:

    Although I have the feeling of having left unfinished almost every mathematical project undertaken, the study of endoscopy and the stabilized trace formula was, in this respect, one of the most unsatisfactory of all. It went on for a very long time without reaching any very cogent conclusions. This now seems with hindsight to have been inevitable. The efforts of a number of excellent mathematicians make it clear that the problems to be solved, many of which remain outstanding, were much more difficult than I appreciated. In particular, the fundamental lemma which is introduced in these notes, is a precise and purely combinatorial statement that I thought must therefore of necessity yield to a straightforward analysis. This has turned out differently than I foresaw.

    Without the kind invitation of Marie-France Vignéras to deliver lectures at the École normale supérieure de jeunes filles, I would never have attempted to communicate the inchoate results at my disposition and I would have continued, no doubt unsuccessfully, to struggle with problems, both local and global, that were beyond me. The lectures were an occasion to clarify and organize the few ideas that I had, and have served as a stimulus to other, more competent, investigators.

Orbital integrals on forms of SL(3) I

This originally appeared in the Am. Jour. Math. 105 (1983), pp. 465- 506.

On principal values on p-adic manifolds (with Diana Shelstad)

This originally appeared in the Lie group representations II, Lecture Notes in Mathematics 41, Springer-Verlag, 1984.

Orbital integrals on forms of SL(3) II (with D. Shelstad)

This originally appeared in the Can. Jour. Math. XLI (1989), pp. 480-507.

On the definition of transfer factors (with D. Shelstad)

This originally appeared in the issue of the Mathematischen Annalen 278 (1987), pp. 219-271 - an issue dedicated to Friedrich Hirzebruch.

Descent for transfer factors (with D. Shelstad)

This originally appeared on pp. 486-563 of volume II of The Grothendieck Festschrift, published in 1990 by Birkhäuser.

Remarks on Igusa theory and real orbital integrals

This originally appeared in The zeta functions of Picard modular surfaces, edited by Robert P. Langlands and Dinakar Ramakrishnan, published by the Centre de Recherches Mathématiques in Montréal, 1992.

Eisenstein series, the trace formula, and the modern theory of automorphic forms

This originally appeared in the proceedings of a conference in Oslo (1987) in honor of Atle Selberg: Number theory, trace formulas, and discrete groups, Academic Press, 1989.

Beyond endoscopy

This paper has appeared in the Shalika volume, published by the Johns Hopkins Univesity Press. The published paper is not exactly the same as that here because the text was modified by the Press, apparently for reasons of economy. Among other things footnotes were removed and this required somewhat brutal measures. The version in this collection is the preferred version.

Un nouveau point de repère dans la theorie des forme automorphes

The following paper is quite informal and it may be some time before I can seriously reflect on the suggestions it contains. I am grateful to Freydoon Shahidi for suggesting that as an interim measure I write the paper for submission to the Canadian Mathematical Bulletin whose editors have, I believe, accepted it.