Piatetski-Shapiro 9704997 The objective of the research funded under this award is to investigate the lifting of generic cuspidal automorphic representations of orthogonal and symplectic groups G to automorphic representations of GL(n). The method that the PI and his collaborators will use is the following. First, they will construct L-functions for G x GL(m). After that, they will apply the converse theorem for GL(n). The L-functions should have the proper functional equation and good analytic properties. This proposal is in the part of mathematics known as the Langlands program. The Langlands program is part of Number Theory. Number Theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished a driving force in creating new mathematics in other diverse parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus; it embodies the modern approach to the study of whole numbers. Modern Number Theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory.
