Math

Author's comments: Some surprise has been expressed that the notes of Jacquet-Langlands have been placed in the same section as the notes on the \(\epsilon\)-factor. There is a good reason for this. Although the notion of functoriality had been introduced in the original letter to Weil, there were few arguments apart from aesthetic ones to justify it. So it was urgent to make a more cogent case. One tool lay at hand, the Hecke theory, in its original form and in the more precise form created by Weil.

Author's comments: This paper is quite informal and I could not immediately 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, where it appeared in volume 50 (2007).

Editorial comments: This was written in 1973. It first appeared as a preprint distributed by the Institute for Advanced Study, and was later (1988) published by the A.M.S. in Math. Surveys and Monographs 31.

Editorial comments: This has not been published before. It was written around 1977, just after A. Knapp and G. Zuckerman had announced their results on reducible unitary principal series, subsequently explained in a talk at the A.M.S. 1977 summer school in Corvallis (pp. 93--105 of the published proceedings of that conference.)