Integradility Problems for Modular Forms on Algebraic Groups

9401026 Hida该奖项资助Haruzo Hida教授以模块化形式进行的持续研究。Hida教授希望在非实场上建立一个模形式理论，与全实场的理论平行。完全真实领域的理论更丰富，因为人们可以将强大的几何方法引入研究。这是数论领域的研究。数论基本上是对整数的研究。在这个奖项下进行的研究通过将整数编码成称为模形式的函数来研究整数的性质。数论是最古老的数学领域之一，但它一直在为这门学科的其他部分选择方向方面发挥着重要作用。在过去的半个世纪里，整数的研究变得更加重要，因为这个理论已经被用来为计算机科学开发新的算法，并为电子产品构建新的纠错码。

9401026 Hida This award funds the continuing research of Professor Haruzo Hida in modular forms. Professor Hida hopes to construct a theory of modular forms over non-real fields that parallels the theory over totally real fields. The theory over totally real fields is richer because one can bring powerful geometric methods into the study. This is research in the field of number theory. Number theory is basically the study of whole numbers. The research done under this award studies properties of the whole numbers by encoding them into functions called modular forms. Number theory is among the oldest fields of mathematics, yet it has always played an important role in choosing directions for the rest of the subject. Within the last half century, the study of whole numbers has become doubly important as the theory has been used to develop new algorithms for computer science and to construct new error correcting codes for electronics.