Mathematical Sciences: Relations on Representation Numbers of Quadradic Forms

该奖项支持L. Walling教授在自同构函数方面的研究。她打算研究由二次型产生的晶格上的级数的傅立叶系数。她还打算研究函数域上的类似情况。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 L. Walling to work in automorphic functions. She intends to study the Fourier coefficients of theta series attached to lattices arising from quadratic forms. She also intends to study the analogous situation over function fields. 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.