L-functions of Several Complex Variables and Automorphic Forms

多个复变量和自守形式的 L 函数

• 批准号: 0140635
• 负责人: Jeffrey Stopple
• 金额: $ 10.3万
• 依托单位: University of California-Santa Barbara
• 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=0140635&HistoricalAwards=false
• 关键词: functions; Several; Complex; Variables; Automorphic

The research of Imamoglu focuses on the analytic theory of L-series of several complex variables. The PI and her collaborators have recently defined Rankin-Selberg Dirichlet series of several complex variables attached to Siegel cusp forms. She proposes to exploit the analytic properties of these series to establish non-vanishing results for special values of Rankin-Selberg convolutions of Fourier_Jacobi coefficients of Siegel forms and to improve bounds for their classical Fourier coefficients. She also proposes to investigate a possible generalization of the classical Dedekind zeta function of a number field to a zeta function of several complex variables.The investigations of this proposal belong to number theory, which is a branch of mathematics that deals with problems involving whole numbers. Mathematicians have discovered that many of the important properties of whole numbers can be encoded into certain objects called "L-functions". These L-functions have their origin in the study of calculus but our understanding of their fundamental properties are far from complete. The PI and her collaborators proposes to investigate the analytic properties of these functions to fill in some of the gaps in our knowledge.

Imamoglu的研究集中在多复变量L-级数的解析理论。PI和她的合作者最近定义了 附于Siegel尖点形式的多复变量的Rankin-Selberg Dirichlet级数。她建议利用这些系列的分析性质来建立Siegel形式的Fourier_Jacobi系数的Rankin-Selberg卷积的特殊值的非零结果，并改进其经典Fourier系数的界。她还建议调查一个可能的推广经典的戴德金zeta函数的一个领域，以zeta函数的几个复变数。调查这一建议属于数论，这是一个分支的数学，处理问题，涉及整数。数学家们已经发现，整数的许多重要性质可以编码到某些称为“L函数”的对象中。这些L-函数起源于微积分的研究，但我们对它们的基本性质的理解还远未完成。PI和她的合作者建议研究这些函数的分析性质，以填补我们知识中的一些空白。