RUI: Arithmetic of Modular Forms and of Diagonal Hypersurfaces

RUI：模形式和对角超曲面的算术

• 批准号: 9401313
• 负责人: Fernando Gouvea
• 金额: $ 7.84万
• 依托单位: Colby College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401313&HistoricalAwards=false
• 关键词: RUI; Arithmetic; Modular; Forms; Diagonal

Gouvea This award funds the investigations of Prof. Fernando Gouvea under the Research in Undergraduate Institutions Program. Prof. Gouvea will study the arithmetic of modular forms and the arithmetic of diagonal hypersurfaces over finite fields. The central topic in the first part of the work is the study of two operators introduced by Atkin. In the second part the investigator will study the simplest cases of arithmetic on abelian varieties. This research falls under the general heading of Number Theory. Number Theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished the driving force to creation of new mathematics in almost all parts of the discipline. One of the philosophies of modern number theory is that many facts about numbers can be studied using calculus and geometry. This approach is very evident in the work of this project since modular forms are studied using calculus and abelian varieties are studied using geometry. This kind of number theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory. ***

古韦亚 该奖项资助Fernando Gouvea教授在本科院校研究计划下的研究。 Gouvea教授将研究有限域上的模形式的算术和对角超曲面的算术。 中心议题在第一部分的工作是研究两个运营商介绍阿特金。 在第二部分调查将研究最简单的情况下算术的阿贝尔品种。 这项研究福尔斯属于数论的总标题。数论是研究整数的性质，是数学最古老的分支。从一开始，数论中的问题就为这门学科的几乎所有部分的新数学的创造提供了动力。现代数论的哲学之一是，关于数字的许多事实都可以使用微积分和几何来研究。 这种方法在本项目的工作中非常明显，因为模形式是使用微积分研究的，阿贝尔变体是使用几何研究的。 这种数论非常技术性和深刻，但它在理论计算机科学和编码理论等领域有着惊人的应用。***