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THE DETERMINATION OF SUBGROUPS IN IDEAL CLASS GROUPS OF REAL QUADRATIC FIELDS 被引量:1

THE DETERMINATION OF SUBGROUPS IN IDEAL CLASS GROUPS OF REAL QUADRATIC FIELDS
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摘要 Series of results about ideal class groups H (m) and class numbers h (m) of real quadratic fields Q (m<sup>1/2</sup>) can be obtained from [6]. Some of them will be shown in this note. We denote by C<sub>n</sub> =Z/nZ the cyclic group of order n. Let m ∈ Z denote a square free positive integer, and let z<sub>1</sub>, z, t ∈Z be arbitrary integers with z<sub>1</sub> odd and t】0.
作者 张贤科
出处 《Chinese Science Bulletin》 SCIE EI CAS 1992年第11期890-893,共4页
关键词 REAL QUADRATIC field IDEAL CLASS group CLASS number REAL QUADRATIC FIELD IDEAL CLASS GROUP CLASS NUMBER
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同被引文献8

  • 1Zhang Xianke,Washington,L.Ideal class groups and their subgroups of real quadratic fields. Scientia Sinica . 1997
  • 2Lu Hong-wen.Divisibility for class numbers of a kind of real quadratic fields, Acta Math. Sinica . 1985
  • 3Cohen,H.,Jr.,Lenstra,H.W.,Jager,H.Heuristics on class groups of number fields. Number theory. Noordwijkerhout 1983, Proceedings . 1984
  • 4Louboutin,S.Arithmetique des Corps Quadratiques Reels et Fractions Continues, (These de doctorat), Paris: Univ. de Paris . 1987
  • 5Mollin R A,Williams H C.Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type(with one possible exception). Journal of Number Theory . 1990
  • 6Cornell, G,Washington. L.Class numbers of cyclotomic fields. Journal of Number Theory . 1982
  • 7Zhang Xianke.Determination of solutions and solvabilities of Diophantine equatioons and quadratic fields. Algebraic Geometry and Algebraic Number Theory . 1992
  • 8张贤科.Criteria of Class Number h(K)=1 for Real Quadratic Number Fields[J].Chinese Science Bulletin,1993,38(4):273-276. 被引量:1

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