Mathematical Sciences: Hans Rademacher Commemorative Conference

数学科学：汉斯·拉德马赫纪念会议

• 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

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.

该项目的重点将是一个会议的影响， Hans Rademacher教授在最近数学领域的研究成果 research. 本次会议的主要议题将包括 模函数，加法数论，和戴德金和， 解析数论 Rademacher成功地扩展了 圆方法获得精确的，收敛的级数表示 非正模形式的傅里叶系数 权重（包括重要的例子p（n））提供了 理论上， 以研究人员的发展为导向的学校 利用黎曼曲面理论和函数的观点， 理论和当代Eichler上同调理论。 他 研究加法数论的更多组合方面 与最近的事态发展有关，包括加西亚-米尔恩 Rogers-Ramanujan恒等式的双射，巴克斯特解 Hard Hexagon模型的证明，以及Hickerson对Mock模型的证明 Theta猜想 最后，他的工作戴德和有关 到最近关于虚二次域的类数的工作， 真实的二次域和全二次域的ζ-函数的值 整宗量的真实的三次域，随机数 一代，以及其他。 该项目将支持Hans Rademacher纪念 会议将于1992年7月21日至25日在宾夕法尼亚州举行 大学 会议的主要议题是模块化的 函数、加法数论、戴德金求和和解析 数论 会议将包括两个邀请会谈 并提供论文会议。