On the exponents of ideal class groups of CM-fields

  • Kuniaki Horie
  • Mitsuko Horie
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1434)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Boyd, D. W., Kisilevsky, H.: On the exponent of the ideal class group of complex quadratic fields. Proc. Amer. Math. Soc. 31, 433–436 (1971)MathSciNetMATHGoogle Scholar
  2. [2]
    Brauer, R.: On the zeta-functions of algebraic number fields. Amer. J. Math. 69, 243–250 (1947)MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Chowla, S.: An extension of Heilbronn’s class-number theorem. Quart. J. Math. 5, 304–307 (1934)CrossRefMATHGoogle Scholar
  4. [4]
    Earnest, A. G.: Exponents of class groups of imaginary abelian number fields. Bull. Austral. Math. Soc. 35, 231–245 (1987)MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Earnest, A. G.: Finiteness theorems for number fields having class groups of given 2-power exponent. In: Mollin, R. A. (ed.) Number theory and applications. Proceedings, Banff Centre 1988. (NATO ASI Series C, vol. 265, pp. 373–380) Dordrecht Boston London: Kluwer Academic 1989Google Scholar
  6. [6]
    Earnest, A. G., Körner, O. H.: On ideal class group of 2-power exponent. Proc. Amer. Math. Soc. 86, 196–198 (1982)MathSciNetMATHGoogle Scholar
  7. [7]
    Horie, K., Horie, M.: CM-fields and exponents of their ideal class groups. Acta Arith. 55 (to appear)Google Scholar
  8. [8]
    Horie (née Hamamura), M.: On absolute class fields of certain algebraic number fields. Nat. Sci. Rep. Ochanomizu Univ. 32, 23–34 (1981)MathSciNetMATHGoogle Scholar
  9. [9]
    Iwasawa, K.: A note on class numbers of algebraic number fields. Abh. Math. Sem. Univ. Hamburg 20, 257–258 (1956)MathSciNetMATHGoogle Scholar
  10. [10]
    Stark, H. M.: Some effective cases of the Brauer-Siegel theorem. Invent. math. 23, 135–152 (1974)MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Uchida, K.: Imaginary abelian number fields of degrees 2m with class number one. In: Proceedings of the international conference on class numbers and fundamental units of algebraic number fields, Katata 1986. (pp. 151–170)Google Scholar
  12. [12]
    Weinberger, P. J.: Exponents of the class groups of complex quadratic fields. Acta Arith. 22, 117–124 (1973)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Kuniaki Horie
    • 1
  • Mitsuko Horie
    • 2
  1. 1.Department of Mathematics (Kyoyobu)Yamaguchi UniversityYoshida, YamaguchiJapan
  2. 2.Department of MathematicsKyushu UniversityFukuokaJapan

Personalised recommendations