Mathematical Sciences: New Models in the Rankin-Selberg Method and Uses of the Metaplectic Group

该奖项支持D. Bump教授在自同构函数方面的研究。他打算扩展Rankin Selberg方法，并研究元塑群的新用途。这些包括对GL(2) n-fold盖上的函数的非唯一Whittaker模型的研究。模形式起源于19世纪中期的非欧几里得几何。因此，数学家和物理学家很早就认识到，许多具有根本重要性的物体在其基本性质上是非欧几里得的。这个领域主要关注关于整数的问题，但在使用几何和分析时，它保留了与历史根源的联系，因此与理论物理中的规范理论和信息论中的编码理论等领域的问题联系在一起。

This award supports the research of Professor D. Bump to work in automorphic functions. He intends to work on extending the Rankin Selberg method and on new uses of the metaplectic group. These include the study of non-unique Whittaker models of theta functions on the n-fold cover of GL(2). Modular forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. 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 and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.