This grant supports Professor Elliott to work in the area of probabilistic number theory. Specifically, this proposal is to study the values of arithmetic functions on prescribed sequences of arithmetic interest. Besides their own merit, such functions bear upon problems in algebra, and apply to the study of algorithms for the factorization of large integers, and so to cryptography. 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.
