Mathematical Sciences: Theory of P-Adic Modular Forms and Hecke Algebras

数学科学：P-Adic模形式和赫克代数理论

• 批准号: 8802001
• 负责人: Haruzo Hida
• 金额: $ 12.68万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802001&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Adic; Modular

The research in this grant concerns the theory of p-adic Hecke algebras. This theory attempts to give a systematic way to construct p-adic L-functions associated with p-adic or complex cusp forms and their Galois representations over power series rings with coefficients in the p-adic integers. Also the principal investigator hopes to find arithmetic relations between these Galois representations and the constructed p-adic L- functions. This theory has been developed for the rational numbers but much remains to be done over general number fields. There will be applications to the Iwasawa theory of imaginary quadratic fields. The p-adic theory of modular forms is the subject of this research. Modular forms are functions that transform in certain ways and are at the center of much research in number theory today. The p-adic theory replaces the usual real or complex numbers with the number theoretic p-adic numbers. Obtaining analogs with the usual theory is a major focus of this research.

本基金的研究涉及p-adic理论 赫克代数 这一理论试图给出一个系统的方法， 构造与p-adic或复相关联的p-adic L-函数 幂级数上的尖形及其Galois表示 系数为p-adic整数的环。 也 首席研究员希望找到算术关系之间 这些伽罗瓦表示和构造的p-adic L- 功能协调发展的 这个理论是为理性的人而发展的 数字，但仍有许多工作要做的一般数字领域。 岩泽的想象力理论 二次域 模形式的p-adic理论是这一主题 research. 模形式是在某些情况下变换的函数。 方法，并且是数论许多研究的中心 今天 p-adic理论取代了通常的真实的或复杂的 与数论中的p-adic数。 获得 与通常理论的类比是本研究的主要焦点。