L-functions of Several Complex Variables and Automorphic Forms

Imamoglu的研究重点是复数变量的l级数的解析理论。PI和她的合作者最近定义了几个附加在西格尔尖形上的复杂变量的Rankin-Selberg Dirichlet系列。她建议利用这些级数的解析性质来建立西格尔形式的傅里叶系数的Rankin-Selberg卷积的特殊值的非消失结果，并改进其经典傅里叶系数的界限。她还建议研究将数字域的经典Dedekind zeta函数推广到多个复变量的zeta函数的可能性。这个建议的研究属于数论，这是数学的一个分支，处理涉及整数的问题。数学家们发现，整数的许多重要性质都可以被编码成某些被称为“l函数”的对象。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远不够。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。

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.