COMPOSITE STUDY IN CLASS FIELD THEORY AND RELATED TOPICS

1.首席调查员于1998年6月组织了一次名为《阶级场理论--百年与展望》的国际会议，获得了与阶级场理论相关的重要信息。他编辑的会议记录目前正在准备出版中。在会议上，调查人员M.Kurihara和Y.Y.Yamamoto，以及合作者H.Nakamura(东京地铁大学)，M.Ozaki(早稻田大学和岛根大学)和H.Suzuki(名古屋U.)做了一个小时的演讲。教授L.Washington(马里兰州大学)、G.Frei(拉瓦尔大学)、J.H.Coates(剑桥大学)、W.Casselman(不列颠哥伦比亚省大学)、Th.Zink(BielefeldU.)和R.Greenberg(美国华盛顿大学)应邀讲授关于岩泽理论、互惠定律的发展、岩泽椭圆曲线理论、朗兰兹计划、关于p-可分群的Dieudonne理论、Greenberg猜想等主题的知识和信息。主要研究人员得到了二面群和循环群的新的简单的“一般多项式族”。作为数论的一个应用，他发展了一种构造二次域上三次类域的新方法，并对这种情况下的“Spiegelungs fenomea”给出了一个清晰的解释。他应邀在La Maison de Franco-Japan的Fermat Colloquum做了一个小时的演讲。研究人员Y.Y.Yamamoto得到了椭圆曲线上正则级数的明确而重要的性质，并通过计算机收集了大量数据，对Taniyama-Shimura猜想给出了很好的解释。

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'.