The focus of this project will be a conference on the impact of the work of Professor Hans Rademacher on recent mathematical research. The major topics of this conference will include modular functions, additive number theory, and Dedekind sums and analytic number theory. Rademacher's successful extension of the circle method to obtain exact, convergent series representations for the Fourier coefficients of modular forms of nonpositive weights (including the important example p(n)) has provided the crucial step linking the results of the number-theoretically oriented school to the developments initiated by researchers using the perspectives of Riemann surface theory and function theory and to the contemporary Eichler cohomology theory. His work on the more combinatorial aspects of additive number theory is related to recent developments, including the Garsia-Milne bijection for the Rogers-Ramanujan identities, Baxter's solution of the Hard Hexagon Model, and Hickerson's proof of the Mock Theta Conjectures. Finally, his work on Dedekind sums is related to recent work on class numbers of imaginary quadratic fields, values of zeta-functions of real quadratic fields and totally real cubic fields at integral arguments, random number generation, and others. This project will support the Hans Rademacher Commemorative Conference to be held from July 21-25, 1992 at Pennsylvania State University. The major topics of the conference are modular functions, additive number theory, and Dedekind sums and analytic number theory. The conference will include both invited talks and contributed paper sessions.
