RUI: The Partition Function and Modular Forms, Gaussian Hypergeometric Series, Modularity of Varieties, Mock Theta Functions, and Polynomial-Exponential Equations

RUI：配分函数和模形式、高斯超几何级数、簇模性、模拟 Theta 函数和多项式指数方程

• 批准号: 0088961
• 负责人: Scott Ahlgren
• 金额: $ 3.66万
• 依托单位: Colgate University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-01 至 2001-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0088961&HistoricalAwards=false
• 关键词: RUI; Partition; Function; Modular; Forms

This award will support the investigator's ongoing research in the field of number theory. For example, the investigator will continue his study of the interplay between the theory of modular forms and partition theory. He will also study the "Gaussian hypergeometric series'' and their relationships to elliptic curves, modular forms, p-adic analysis, arithmetic geometry, and combinatorics. In addition, the award will enable the investigator to expand his efforts in undergraduate education and research.Number Theory is a very old branch of mathematics which has its roots in the study of the whole numbers. In modern times it has become an important tool in many applied endeavors. For example, cryptosystems which enable secure transmission of data over the internet are based on Number Theory, as are error correcting codes for reliable data transmission.

该奖项将支持研究人员在数论领域正在进行的研究。 例如，研究者将继续研究模形式理论和划分理论之间的相互作用。 他还将研究“高斯超几何级数”及其与椭圆曲线，模形式，p-adic分析，算术几何和组合数学的关系。 此外，该奖项将使调查员扩大他在本科教育和研究方面的努力。数论是数学的一个非常古老的分支，其根源在于对整数的研究。 在现代，它已成为许多应用领域的重要工具。 例如，能够在互联网上安全传输数据的密码系统是基于数论的，用于可靠数据传输的纠错码也是如此。