The relative trace formula and central L-values

相对迹线公式和中心 L 值

• 批准号: 0902145
• 负责人: Andrew Knightly
• 金额: $ 13.72万
• 依托单位: University of Maine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0902145&HistoricalAwards=false
• 关键词: relative; trace; formula; central; values

The purpose of the proposed research is to establish new explicit identities involving the central values of L-functions and other data attached to automorphic forms. The relative trace formula is a technique which expresses period integrals of automorphic forms on a given group in terms of orbital integrals on the group. Depending on the setup, the period integrals can give desirable spectral information, like Fourier coefficients or L-values. One example is the GL(2) Fourier trace formula of Kuznetsov, which has become ubiquitous in analytic number theory with applications to such diverse important problems as bounding sums of Kloosterman sums, moments of the Riemann zeta function, and subconvexity for modular L-functions. The PI and his collaborator C. Li will develop other Fourier trace formulas, and also directly investigate various averages of L-functions using the relative trace formula.This project is in number theory, which is the study of the integers and their algebraic properties. According to a conjecture of Langlands, the algebraic structure of the rational numbers, as captured by the Galois group, is encoded by modular forms. These are functions in advanced calculus which exhibit special symmetries. The proposed research will deepen our understanding of modular forms.

所提出的研究的目的是建立新的明确的身份，涉及的中心值的L-函数和其他数据附加到自守形式。 相对迹公式是一种将给定群上自守形式的周期积分表示为该群上的轨道积分的技术。 根据设置，周期积分可以给出所需的光谱信息，如傅立叶系数或L值。 一个例子是库兹涅佐夫的GL（2）傅立叶迹公式，它在解析数论中已经变得无处不在，并应用于各种重要问题，如Kloosterman和的有界和，Riemann zeta函数的矩，以及模L函数的次凸性。 PI和他的合作者C。李将开发其他傅立叶迹公式，也直接研究各种平均的L-函数使用相对迹公式.这个项目是在数论，这是研究整数和它们的代数性质. 根据朗兰兹的一个猜想，有理数的代数结构，如伽罗瓦群所捕获的，是由模形式编码的。 这些函数在高等微积分中表现出特殊的对称性。 本文的研究将加深我们对模式的理解。