| Project/Area Number |
08304004
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | TOKYO METROPOLITAN UNIVERSITY |
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Principal Investigator |
MIYAKE Katsuya TOKYO METROPOLITAN UNIVERSITY,MATH., PROFESSOR, 理学研究科, 教授 (20023632)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAMOTO Yoshiyuki OSAKA UNIVERSITY,MATH., PROFESSOR, 理学研究科, 教授 (90028184)
MORITA Yasuo TOHOKU UNIVERSITY,MATH., PROFESSOR, 理学研究科, 教授 (20011653)
KOIKE Masao kYUSHU UNIVERSITY,MATH.SCI., PROFESSOR, 数理学研究科, 教授 (20022733)
KITAOKA Yoshiyuki NAGOYA UNIVERSITY,POLYMATH., PROFESSOR, 多元数理研究科, 教授 (40022686)
NAKAMULA Ken TOKYO METROPOLITAN UNIVERSITY,MATH., PROFESSOR, 理学研究科, 教授 (80110849)
足立 恒雄 早稲田大学, 理工学部, 教授 (60063731)
栗原 将人 東京都立大学, 理学部, 助教授 (40211221)
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| Project Period (FY) |
1996 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥4,400,000 (Direct Cost: ¥4,400,000)
Fiscal Year 1998: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1997: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | CLASS FIELD THEORY / CLASS NUMBERS / QUADRATIC FIELDS / CUBIC FIELDS / DIHEADRAL EXTHENSIONS / UNITS / HYPERGEOMETRIC POLYNOMIALS / TATE CONJECTURE / 一般Lucas数列 / 算術的有限部分群 / Batyrev-Manin予想 / ゼータ関数 / 一次分数変換 / 奇数次巡回拡大 / 算術的三角群 |
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| Research Abstract |
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'.
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