Preamble

Summary

Over the last few years, Arthur has formulated some extremely precise conjectures generalising Jacquet's conjectures for GL(n), on the description of square integrable automorphic forms (see [J], [A2], [A3], [A4]). The origin of these conjectures can be found in his work on the trace formula and their point of departure goes back to Langlands' work (see Arthur's Corvallis talk [A1]). It is probable that the full force of the constructions of these automorphic forms as residues of Eisenstein series has not been exploited. It is thus important to fully understand the basic book [L]; this was our main motivation. Since Langlands wrote the material of [L] (around 1967), several authors have already given personal presentations (Godement [G], Harish-Chandra [HC], Osborne-Warner [OW]). Morris extended Langlands' results to the function field case ([M1] and [M2]).

The following notes are a reworking of the book [L] and an ameliorated (and unified) version of talks which we gave in the ‘automorphic’ seminar (Paris 7/ENS). A seminar cannot exist without critical auditors: we wish to thank P. Barrat, J. -R Labesse, P. Perrin (who also gave some talks on this subject), A. -M. Aubert, C. Blondel, L. Clozel, G. Henniart, G. Laumon (for whom the goal of the seminar was to render entirely obscure what was already not particularly clear), M.-F. Vignéras and D. Wigner.