Mathematical Sciences: Automorphic Forms and Representation Theory

数学科学：自守形式和表示论

• 批准号: 8715402
• 负责人: Thomas Hales
• 金额: $ 3.52万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-12-01 至 1990-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8715402&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Automorphic; Forms; Representation

This research deals with the subject of automorphic forms and representation theory using geometric methods. The main problem is to obtain the analytic continuation and functional equation of the Hasse-Weil zeta function of Shimura varieties. The object is to express these zeta functions in terms of automorphic L-functions. Then one must obtain the transformation laws for these automorphic L-functions. This research will study the generating functions for the number of solutions of systems of polynomial equations modulo all the primes. The properties of these functions will give an immense amount of information concerning the solution to the corresponding set of Diophantine Equations. Number Theory has as one of its chief components the study of Diophantine Equations, that is the solution of sets of equations in integers.

本研究用几何方法研究了自同构形式和表示理论。主要问题是得到Shimura变种的Hasse-Weil Zeta函数的解析延拓和函数方程。目的是用自同构的L函数来表示这些zeta函数。然后得到这些自同构L函数的变换规律。本研究将研究模为所有素数的多项式方程组解的个数的母函数。这些函数的性质将给出大量关于相应丢番图方程组的解的信息。数论的主要组成部分之一是研究丢番图方程，即求解整数中的方程组。