This grant supports the research of Professor P. Sarnak as principal investigator and Dr. Zeev Rudnick as a post-doctoral associate. Professor Sarnak will work on the spectral theory of automorphic forms and its applications to number theory and combinatorics. He hopes to make progress towards the general Ramanujan conjecture. Dr. Rudnick is working in automorphic forms. He intends to apply techniques derived from the study of automorphic forms to counting integer points on affine varieties. He is also investigating the behavior of Euler products. This is research in the field of number theory broadly conceived. 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.
