ArticleOriginal scientific text

Title

Quadratic function fields whose class numbers are not divisible by three

Authors 1

Affiliations

  1. Department of Mathematics, Yokohama City University, 22-2, Seto, Kanazawa-ku, Yokohama, 236-0027 Japan

Bibliography

  1. E. Artin, Quadratische Körper im Gebiet der höheren Kongruenzen I und II, Math. Z. 19 (1923), 153-246.
  2. G. Cornell, Abhyankar's lemma and the class group, in: Number Theory, Carbondale, 1979, M. Nathanson (ed.), Lecture Notes in Math. 751, Springer, New York, 1981, 82-88.
  3. G. Cornell, Relative genus theory and the class group of l-extensions, Trans. Amer. Math. Soc. 277 (1983), 321-429.
  4. B. Datskovsky and D. J. Wright, Density of discriminants of cubic extensions, J. Reine Angew. Math. 386 (1988), 116-138.
  5. H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields II, Proc. Roy. Soc. London Ser. A 322 (1971), 405-420.
  6. C. Friesen, Class number divisibility in real quadratic function fields, Canad. Math. Bull. 35 (1992), 361-370.
  7. M. Hall, The Theory of Groups, Macmillan, New York, 1959.
  8. P. Hartung, Proof of the existence of infinitely many imaginary quadratic fields whose class numbers are not divisible by three, J. Number Theory 6 (1976), 276-278.
  9. K. Horie, A note on basic Iwasawa λ-invariants of imaginary quadratic fields, Invent. Math. 88 (1987), 31-38.
  10. H. Ichimura, On the class groups of pure function fields, Proc. Japan Acad. 64 (1988), 170-173; corrigendum, ibid. 75 (1999), 22.
  11. K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257-258.
  12. I. Kimura, On class numbers of quadratic extensions over function fields, Manuscripta Math. 97 (1998), 81-91.
  13. T. Nagell, Über die Klassenzahl imaginär-quadratischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 1 (1922), 140-150.
  14. P. Roquette and H. Zassenhaus, A class rank estimate for algebraic number fields, J. London Math. Soc. 44 (1969), 31-38.
  15. M. Rosen, The Hilbert class fields in function fields, Exposition. Math. 5 (1987), 365-378.
  16. D. Shanks, The simplest cubic fields, Math. Comp. 28 (1974), 1137-1157.
  17. Y. Yamamoto, On unramified Galois extensions of quadratic number fields, Osaka J. Math. 7 (1970), 57-76.
Pages:
181-190
Main language of publication
English
Received
1999-02-12
Published
1999
Exact and natural sciences