Families of L-functions and Applications

L 函数族及其应用

• 批准号: 0202982
• 负责人: Peter Sarnak
• 金额: $ 32.53万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0202982&HistoricalAwards=false
• 关键词: Families; functions; Applications

The investigator will continue his study of L-functions. Specifically the problem of a 'subconvex' estimate for general automorphic L-functions. These have wide applications to classical problems in number theory (e.g. Hilbert's 11-th problem on representing integers in a number field by a quadratic form) and to eigenfunctions on arithmetic surfaces. The use of the families of L-functions and symmetries associated with them is crucial. This project is concerned with the study of mathematical objects called zeta functions. They encode deep information about the arithmetic and geometry which lie at their definition. Understanding the functions has far reaching applications to the theory of whole numbers (and prime numbers) and more surprisingly to some foundational problems in quantum theory.

研究者将继续他对 L 功能的研究。 特别是一般自同构 L 函数的“次凸”估计问题。 它们广泛应用于数论中的经典问题（例如，希尔伯特关于用二次形式表示数域中的整数的第 11 个问题）和算术曲面上的本征函数。 L 函数族及其相关对称性的使用至关重要。该项目涉及称为 zeta 函数的数学对象的研究。 它们对定义中的算术和几何的深层信息进行编码。 理解这些函数对整数（和素数）理论有着深远的应用，更令人惊讶的是对量子理论中的一些基本问题的应用。