This award supports the research in Analytic Number Theory of Professor Boris Datskovsky of Temple University. His project is to investigate properties of prehomogeneous vector spaces and zeta functions associated to them. These spaces have permitted the attainment of new results on the density of discriminants of cubic fields, as well as the density of class numbers for imaginary quadratic fields. 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, the field has had a new rebirth.
