COMPOSITE STUDY IN CLASS FIELD THEORY AND RELATED TOPICS

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1. The head investigator organized an international conference 'Class Field Theory - Its centenary and prospect' in June, 1998, and obtained important informations related to class field theory. The proceedings editted by him is now under preparation for publication. In the conference, Investigators M.Kurihara and Y.Yamamoto, and Cooperators H.Nakamura (Tokyo Metro-U.), M.Ozaki (Waseda U.and Shimane U.) and H.Suzuki (Nagoya U.) gave one-hour talks.2. Professors L.Washington (U.Maryland), G.Frei (Laval U.), J.H.Coates (CambridgeU.), W.Casselman (U.British Columbia), Th.Zink (BielefeldU.) and R.Greenberg (U.Washington) were invited by the grant to teach their knowledge and informations on the subjects, Iwasawa Theory, Development of Reciprocity Law, Iwasawa Theory of Elliptic Curves, Langlands Program, Dieudonne Theory on p-divisible Groups, Greenberg Conjectures, etc.3. The head investigator obtained new simple 'generic families of polynomials' for dihedal groups and cyclic groups. As an application to number theory, he developed a new method of construction of class fields of degree 3 over quadratic field and could give a clear explanation for the 'Spiegelungs fenomena' in this case. He was invited to give an one-hour talk in Fermat Colloquium at La Maison de Franco-Japonaise.4. Investigator Y.Yamamoto obtained clear and important properties of canonical series on elliptic curves, collected a good amount of data by computer and gave a fine explanation for 'Taniyama-Shimura Conjecture'.