Yale and Converse Theorem
Starting in 1977, Ilya divided his time between Tel-Aviv University and Yale, directing doctoral dissertations in both places. One of his major works at Yale dealt with the converse theorem which establishes a link between automorphic forms on n by n matrix groups and zeta functions.
For n = 1 this theorem is classical. The assertion for n = 2 was proved by André Weil, and the novel version for n = 3 was conceived by Piatetski-Shapiro while he was still a refusenik in the Soviet Union. It took another 25 years and works with other collaborators, in particular his student James Cogdell, before the suitably flexible and powerful general case was completed.
The converse theorem has played a role in many of the results known in the direction of the principle of functoriality of Langlands.
Read more about this topic: Ilya Piatetski-Shapiro
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