Integradility Problems for Modular Forms on Algebraic Groups

9401026希达 该奖项资助Haruzo希达教授以模块化形式继续进行研究。 希达教授希望在非真实的领域上建立一个模形式的理论，该理论与完全真实的领域上的理论相似。 全真实的域上的理论由于可以引入强有力的几何方法而更加丰富。 这是数论领域的研究。 数论基本上是对整数的研究。 在该奖项下完成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。数论是数学中最古老的领域之一，但它在选择其他学科的方向方面一直发挥着重要作用。 在过去的半个世纪，研究整数已成为双重重要的理论已被用来开发新的算法，计算机科学和构造新的纠错码的电子。

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.