Mathematical Sciences: Eisenstein Series on the Metaplectic Group, Special Values of Automorphic L-Functions and Functional Equations

该奖项支持在自守形式的研究 斯坦福大学教授丹尼尔·邦普。邦普博士的大部分 计划中的研究是与S.油炸- 位于圣克鲁斯的加州大学的贝格和J.霍夫- 布朗大学的斯坦。他们利用了 一类Eisenstein自守L-函数的二次扭 系列的亚群，通过应用到这些爱森斯坦 Novodvorsky提出的积分卷积。这 结果在狄利克雷级数与已知极点，导致 一种新的非零定理他们已经获得了一个 结果，当结合Kolyvagin最近的工作时， 椭圆曲线上Birch-Swinnerton-Dyer定理的应用 曲线. 非欧平面几何始于19世纪初 世纪作为一个数学的好奇心，但在年底， 世纪，数学家们已经意识到， 基本的重要性是非欧几里德在其基本性质。 对非欧平面几何的详细研究， 上升到现代数学的几个分支，其中 模和自守形式的研究是最活跃的研究之一。 此字段主要涉及有关 整数，但在其使用几何和分析，它 与其历史根源保持联系。

This award supports the research in Automorphic Forms of Professor Daniel Bump of Stanford University. Much of Dr. Bump's planned research is a continuation of joint work with S. Fried- berg of the University of California at Santa Cruz and J. Hoff- stein of Brown University. They exploit the occurrence of quadratic twists of automorphic L-functions of certain Eisenstein series on the metaplectic group, by applying to these Eisenstein series an integral convolution introduced by Novodvorsky. This results in a Dirichlet series with known poles, leading to nonvanishing theorems of a new type. They have already obtained a result which, when combined with recent work of Kolyvagin, has applications to the Birch-Swinnerton-Dyer conjectures on elliptic curves. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of Modular and Automorphic Forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of Geometry and Analysis, it retains connection to its historical roots.