1. Ph.D. Thesis
6. Base change
14. Visual material
The letter to Weil included a number of striking conjectures which eventually changed much of the direction of research in automorphic forms. Some of their consequences were explained in a graduate course given at Princeton in the spring of 1967, and then things were put in a somewhat wider context in a series of lectures at Yale later that Spring. These notes were previously published as the first of the Yale Mathematical Monographs.
Langlands Comments: This monograph was based on lectures given early in April of 1967 at Yale University, thus several months after the letter to Weil. Nonetheless it is reticent about the conjectures formulated in that letter. Results are formulated in terms of the dual group introduced there, which could for the groups of the lectures be introduced without any reference to the Galois group because only split groups are treated. There is, however, only the slightest of allusions to any generalization of class-field theory: the observations that what can be done for one reductive group should be done for all and that the identification of an automorphic
The formula (6), which is established in sufficient generality to verify the convergence of the Euler products, is not established in general, although it is surmised that it is generally true. This was, indeed, proved a little later in complete generality and, so far as I know, quite independently by Ian MacDonald (Spherical functions on a group of
The formula referred to as the formula of Gindikin-Karpelevich was, indeed, proved in general by them, but had first been discovered by Bhanu-Murty and proved by him for the special linear group over R in мера Планшереля для фактор-пространства SL(n,R)/SO(n,R), ДАН 133 (1960).
Although the notes for the lectures were available as a preprint at the time they were delivered or shortly thereafter, the monograph did not appear until 1970. Apart from the addition of one or two footnotes and the correction of misprints and slips of the pen, there were no alterations.
Gelbart and Shahidi have written a useful survey of the theory of automorphic