Mathematical Sciences: Theory of P-adic Hecke Algebras and Iwasawa Theory for CM Fields

数学科学：P-adic Hecke 代数理论和 CM 场 Iwasawa 理论

• 批准号: 9100704
• 负责人: Haruzo Hida
• 金额: $ 15.03万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100704&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; adic; Hecke

Professor Hida will work on the theory of p-adic Hecke algebras and their applications to Iwasawa theory of CM fields. He will also work on studying forms of half integral weight over totally real fields, the construction of p-adic symmetric square L- functions and their application to the cyclotomic Z-p tower of these fields. This project falls into the general area of arithmetic geometry -a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.

Hida教授将研究p进Hecke代数理论及其在CM场的Iwasawa理论中的应用。他还将研究全实场上的半积分权的形式，p进对称方形L-函数的构造及其在这些场的分圈Z-p塔中的应用。这个项目属于算术几何的一般领域，这门学科融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。