Integradility Problems for Modular Forms on Algebraic Groups

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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.