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1999 Fiscal Year Final Research Report Summary

Research on the reciprocity law of local fields

Research Project

Project/Area Number 09640045
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKagawa University

Principal Investigator

NAITO Hirotada  Kagawa University of Education, A.P., 教育学部, 助教授 (00180224)

Co-Investigator(Kenkyū-buntansha) NAKAJIMA Shoichi  Gakushuin, Science, P., 理学部, 教授 (90172311)
Project Period (FY) 1997 – 1999
KeywordsNumber Theo / local field
Research Abstract

We determine all extensions over the rational p-adic fields which are generated by 3 -division points of elliptic curves, We see that there are three fields which are not generated by such points. As an application, we construct algebraic number fields whose Galois group over the rational number field are isomorphic to the general linear group of degree two over the prime field of three elements with some local conditions ( decomposition law).
We construct infinitely many imaginary quadratic extensions over the fixed totally real number fields such that their relative class numbers are indivisible by the fixed odd prime with some loca conditions.
We rediscover algebraic number fields such 'that their Dedekind zeta functions coincide but they are not conjugate, in the Galois extentions over the rational number fields whose Galois group over the rational number field are isomorphic to the general linear group of degree two over the prime field of p elements. Moreover we prove that the non p parts of the ideal class groups are isomorphic each other.

  • Research Products

    (2 results)

All Other

All Publications (2 results)

  • [Publications] 内藤浩忠: "Stark^新谷予想の紹介"津田塾大学整数論シンポジウム報告集(第5回). 1-13 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hirotada NAITO: "An Introduction of Stark-Shintani Conjecture Reports of Symposium on Number Theory"Tsuda College. (in Japanese). 1-13 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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