Remarks on Igusa theory and real orbital integrals
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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 ϵ-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.
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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).
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Editorial comments: The letter to Weil that saw the birth of the L-group was written in January 1967. Somewhat later that same year, Roger Godement asked Langlands to comment on the Ph.D. thesis of Hervé Jacquet. His reply included a number of conjectures on Whittaker functions for both real and p-adic reductive groups. These were later to be proven, first in the p-adic case by Shintani for GLn and Casselman Shalika in general, and much later in the real case by a longer succession of people.