Mathematical Sciences: Hans Rademacher Commemorative Conference

数学科学：汉斯·拉德马赫纪念会议

基本信息

批准号：
9123821
负责人：
David Bressoud
金额：
$ 1万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1992
资助国家：
美国
起止时间：
1992-06-01 至 1993-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123821&HistoricalAwards=false
关键词：
Mathematical Sciences Hans Rademacher Commemorative

项目摘要

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.

该项目的重点将是汉斯·拉德马赫教授对最近数学研究的工作的影响。这次会议的主要主题将包括模块化函数，添加数理论以及Dedekind总和和分析数理论。 Rademacher成功扩展了圆形方法，以获取非阳性权重模块化形式的傅立叶系数（包括重要的示例p（n））的傅立叶系数（包括重要的示例p（n））提供了关键步骤，将数字导向学校的结果与研究人员启动的发展相关的研究人员使用Riemann表面理论和功能理论和功能理论的研究角度联系起来。他在添加数理论的更加组合方面的工作与最近的发展有关，包括Rogers-Ramanujan身份的Garsia-Milne Bivactions，Baxter对Hard Hexagon模型的解决方案以及Hickerson证明了Mock Theta猜想的证明。最后，他在Dedekind总和上的工作与最新的虚构二次领域的班级数量，真实二次字段的Zeta函数值以及在整体参数，随机数生成等上完全真实的立方字段有关。该项目将支持汉斯·拉德马赫（Hans Rademacher）纪念会议，该会议将于1992年7月21日至25日在宾夕法尼亚州立大学举行。会议的主要主题是模块化函数，添加剂数理论以及Dedekind总和和分析数理论。会议将包括受邀的会谈和撰写纸质会议。