Problems in Analytic Theory of L-functions and Automorphic Forms

9700488 Stopple/Imamoglu该奖项资助第二位指定的主要研究者在以下主题上的研究。首先，她提出研究从经典模形式到Siegel模形式的一系列结构提升。其次，她建议建立一个克罗内克极限公式的辛群的程度4。这涉及到寻找Siegel Eisenstein级数关于其极点的Laurent级数展开。这样的结果可以应用于算术和几何。第三，与J. Hoffstein，她提出发展一个广义的元形式。这些新的形式，在元形式的情况下，预计将导致惊人的结果，在理论的L-功能。最后，与L.瓦林，她建议工作的广义雅可比θ函数。这些theta函数也可以用来作出一个适当的斋藤-黑川猜想，因为它们提供了一个建设性的例子，这样一个电梯。本文的研究属于数论中的一般数学领域福尔斯。数论有其历史根源，在研究整个数字，解决这样的问题，如那些处理整除一个整数由另一个。它是数学中最古老的分支之一，几个世纪以来，人们纯粹出于美学的原因而追求它。然而，在过去的半个世纪，它已成为一个不可或缺的工具，在不同的应用领域，如数据传输和处理，通信系统。

9700488 Stopple/Imamoglu This award funds research by the second named principal investigator on the following topics. First, she proposes to investigate a series of conjectural liftings from classical modular forms to Siegel modular forms. Second, she proposes to establish a Kronecker limit formula for the symplectic group of degree 4. This involves finding the Laurent series expansion of Siegel Eisenstein series about its pole. Such a result would have applications to arithmetic and geometry. Third, with J. Hoffstein, she proposes to develop a generalization of metaplectic forms. These new forms, as in the case of metaplectic forms, are expected to lead to striking results in the theory of L-functions. Last, jointly with L. Walling, she proposes to work on generalized Jacobi theta functions. These theta functions can also be used to make an appropriate Saito-Kurokawa conjecture since they provide a constructive example of such a lift. This research falls into the general mathematical field of Number Theory. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.