Mathematical Sciences: Hans Rademacher Commemorative Conference

该项目的重点将是召开一次会议，讨论Hans Rademacher教授的工作对最近数学研究的影响。本次会议的主要议题将包括模函数、可加数论、戴德金和和解析数论。Rademacher成功的推广圆法得到精确，非正权模形式的傅里叶系数的收敛级数表示（包括重要的例子p(n)）提供了关键的一步，将数论导向学派的结果与研究人员利用黎曼曲面理论和函数理论的观点所发起的发展以及当代艾希勒上同调联系起来理论。他在可加数论的组合方面的工作与最近的发展有关，包括罗杰斯-拉马努金恒恒论的Garsia-Milne双射，巴克斯特对硬六边形模型的解，以及希克森对模拟Theta猜想的证明。最后，他关于Dedekind和的工作与最近关于虚二次域的类数、实二次域和全实三次域在整参数下的ζ函数值、随机数生成等方面的工作有关。该项目将支持将于1992年7月21日至25日在宾夕法尼亚州立大学举行的汉斯·拉德马赫纪念会议。会议的主要议题是模函数、可加数论、戴德金和和解析数论。会议将包括邀请演讲和论文会议。

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.