Special Values of L Functions and Functoriality

L 函数和函子性的特殊值

• 批准号: 0500392
• 负责人: Stephen Rallis
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0500392&HistoricalAwards=false
• 关键词: Special; Values; Functions; Functoriality

1.For Mathematicians Stephen Rallis's work presents two methods to determine functoriality from a classical group to Gl(n). This is done by applying the Converse Theorem coupled with an effective theory of good L functions. The second method is by use of the relative trace formula. The ideas are based on an earlier theory of automorphic descent. He develops with the descent formalism ways to constructCap modules for classical groups. Also the aforementioned theory of L functions allows a procedure to relate nonvanishing of Bessel periods to the nonvanishingof tensor L functions on classical groups.2. For the general public Stephen Rallis's research uses systematically the basic principles of symmetry to investigate fundamental problems in number theory. Incredibly basic problems such as the celebrated Fermat Last Conjecture require such ideas. Stephen Rallis develops various types of symmetry (in a mathematical way) that make up this subject. The main emphasis is to find new ways to show the nonnegativity of self dual automorphic L functions for Gl(n) and other classical groups at the center of symmetry of the functional equation. Also he develops new period conditions to analyze these special values.This is important for the various arithmetic, analytic and geometric ideas tied to nonvanishing of L functions at specific points. This work trains graduate students in mathematical research.

1.对于数学家来说，Stephen Rallis的工作提出了两种方法来确定从经典群到Gl（n）的函性。这是通过应用匡威定理加上一个有效的理论良好的L功能。第二种方法是利用相对迹公式。这些想法是基于早期的自守血统理论。他发展了下降形式主义的方法来构建经典群的Cap模块。此外，上述理论的L功能允许一个程序，以有关非零的贝塞尔周期的nonvanishingof张量L功能的经典群.对于一般公众斯蒂芬拉利斯的研究系统地使用对称性的基本原则，以调查数论的基本问题。令人难以置信的基本问题，如著名的费马最后猜想需要这样的想法。Stephen Rallis发展了各种类型的对称性（以数学的方式），构成了这个主题。重点是寻找新的方法来证明自对偶自守L函数对Gl（n）和其他经典群在函数方程对称中心处的非负性。此外，他制定了新的时期条件，以分析这些特殊的价值观。这是重要的各种算术，分析和几何思想绑在非零的L功能在特定的点。这项工作培养研究生在数学研究。