Mathematical Sciences: L-functions of Automorphic Forms and Applications

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This grant supports the work of Dr. Piatetski-Shapiro to work on projects related to Langland's program. These projects include the problem of unitarity under functorial lifting and is related to the failure of the generalized Ramanujan conjecture. The second project is devoted to a problem of lifting from classical groups to GL(n). The third project is devoted to modelling Langland's correspondence over a finite field. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.