A note on Hilbert class fields of algebraic number fields

  • K. Györy
  • W. Leahey


Abelian Variety Number Field Class Number Automorphic Function Algebraic Number Field 
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  1. [1]
    A. Borel, S. Chowla, C. S. Herz, K. Iwasawa, J-P. Serre, Seminar on complex multiplication,Lecture Notes in Math.,21, Springer Verlag (1966).Google Scholar
  2. [2]
    E. Brown andC. J. Parry, The imaginary bicyclic biquadratic fields with class-number 1,J. Reine Angew. Math.,266 (1974), 118–120.MathSciNetzbMATHGoogle Scholar
  3. [3]
    K. Győry, Sur une classe des corps de nombres algébriques et ses applications,Publ. Math. Debrecen,22 (1975), 151–175.MathSciNetGoogle Scholar
  4. [4]
    H. Hasse,Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil I, Zweite Auflage (Würzburg, 1965).Google Scholar
  5. [5]
    H. Hasse,Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag (Berlin, 1952).zbMATHGoogle Scholar
  6. [6]
    H. L. Montgomery andP. J. Weinberger, Notes on small class numbers,Acta Arith.,24 (1974), 529–542.MathSciNetzbMATHGoogle Scholar
  7. [7]
    G. Shimura andY. Taniyama, Complex multiplication of abelian varieties and its applications to number theory,Publ. Math. Soc. Japan, No.6 (Tokyo, 1961).Google Scholar
  8. [8]
    G. Shimura, Automorphic functions and number theory,Lecture Notes in Math.,54, Springer Verlag, (1968).Google Scholar
  9. [9]
    G. Shimura, Introduction to the arithmetic theory of automorphic functions,Publ. Math. Soc. Japan, No.11 (Iwanami-Princeton, 1971).Google Scholar
  10. [10]
    H. M. Stark, A complete determination of the complex quadratic fields of class-number one,Michigan Math. J.,14 (1967), 1–27.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    H. M. Stark, Some effective cases of the Brauer-Siegel therorem,Inventiones Math.,23 (1974), 135–152.zbMATHCrossRefGoogle Scholar
  12. [12]
    H. M. Stark, On complex quadratic fields with class-number two,Math. Comp.,29 (1975), 289–302.MathSciNetzbMATHGoogle Scholar
  13. [13]
    T. Tatuzawa, On a theorem of Siegel,Japanese J. Math.,21 (1951), 163–178.MathSciNetzbMATHGoogle Scholar
  14. [14]
    K. Uchida, Class numbers of imaginary abelian number fields, II,Tôhoku Math. J.,23 (1971), 335–348.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    K. Uchida, Relative class numbers of normal CM-fields,Tôhoku Math. J.,25 (1973), 347–353.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    H. Weber,Lehrbuch der Algebra, III, Zweite Auflage (Braunschweig, 1908).Google Scholar
  17. [17]
    H. G. Zimmer, Computational problems, methods and results in algebraic number theory,Lecture Notes in Math.,262 Springer Verlag (1972).Google Scholar

Copyright information

© Akadémiai Kiadó 1977

Authors and Affiliations

  • K. Györy
    • 1
  • W. Leahey
    • 2
  1. 1.Department of MathematicsUniversity of DebrecenDebrecenHungary
  2. 2.Department of mathematicsUniversity of Texas at el PasoEl PasoUSA

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