Mathematical Sciences: Hans Rademacher Commemorative Conference

这个项目的重点将是一个关于汉斯·拉德马赫教授的工作对最近数学研究的影响的会议。本次会议的主要议题将包括模函数、加法数论、德德金德和与解析数论。Rademacher成功地将圆法推广到精确解，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))提供了将数论学派的结果与研究人员利用Riemann曲面论和函数论的观点以及当代Eichler上同调理论的发展联系起来的关键一步。他在加法数论的更多组合方面的工作与最近的发展有关，包括对Rogers-Ramanujan恒等式的Garsia-Milne双射，Baxter的硬六角模型的解，以及Hickerson对Mock Theta猜想的证明。最后，他关于Dedekin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的Zeta函数的值、随机数生成等方面的工作有关。该项目将支持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、加法数论、德德金德和与解析数论。会议将包括特邀演讲和来稿论文两部分。

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.