On the Functional Equations satisfied by Eisenstein series, mimeographed notes

In these days of dizzying scientific progress some apology is called for when offering to the mathematical public a work written twelve years ago. It certainly bears the stamp of a juvenile hand, and I had always hoped to revise it, but my inclination to a real effort grew ever slighter, and the manuscript was becoming an albatross about my neck. There were two possibilities: to forget about it completely, or to publish it as it stood; and I preferred the second. There were, when it was first written, other reasons for delaying publication. The study of Eisenstein series is a preliminary to the development of a trace formula, and the trace formula has been a long time evolving. Not only does it present serious analytic difficulties, but also the uses to which it should be put have not been clear. A sustained attack on the analytic difficulties is now being carried out, by Arthur and others, and, thanks to a large extent to developments within the theory of Eisenstein series itself, we now have a clearer picture of the theorems that will flow from the trace formula. However a great deal remains to be done, and a complete treatment of Eisenstein series, even imperfect, may be useful to those wishing to try their hand at developing or using the trace formula. Much of the material in §2–§6 is included in Harish–Chandra’s notes (Lecture Notes 62). He