This award supports the research in Analytic Number Theory of Professor Adolf Hildebrand of the University of Illinois at Urbana. Dr Hildebrand intends to investigate irregularities in the distribution of primes and probabilistic models for the sequence of primes that might explain such irregularities. He also plans to continue work on the distribution of additive and multiplicative arithmetic functions on subsets of the set of positive integers, and to study additive properties of integer sets with a multiplicative structure. The field of Analytic Number Theory applies to the discrete realm of the whole numbers the techniques of Analysis, dependent on the notions of continuity and limit, originating in Calculus. The idea of using continuous methods to investigate the discrete is two centuries old, but with the work of the modern analytic number theorists such as Professor Hildebrand, the field has had a new rebirth.
