ArticleOriginal scientific text
Title
Quadratic function fields whose class numbers are not divisible by three
Authors 1
Affiliations
- Department of Mathematics, Yokohama City University, 22-2, Seto, Kanazawa-ku, Yokohama, 236-0027 Japan
Bibliography
- E. Artin, Quadratische Körper im Gebiet der höheren Kongruenzen I und II, Math. Z. 19 (1923), 153-246.
- 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.
- G. Cornell, Relative genus theory and the class group of l-extensions, Trans. Amer. Math. Soc. 277 (1983), 321-429.
- B. Datskovsky and D. J. Wright, Density of discriminants of cubic extensions, J. Reine Angew. Math. 386 (1988), 116-138.
- H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields II, Proc. Roy. Soc. London Ser. A 322 (1971), 405-420.
- C. Friesen, Class number divisibility in real quadratic function fields, Canad. Math. Bull. 35 (1992), 361-370.
- M. Hall, The Theory of Groups, Macmillan, New York, 1959.
- 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.
- K. Horie, A note on basic Iwasawa λ-invariants of imaginary quadratic fields, Invent. Math. 88 (1987), 31-38.
- H. Ichimura, On the class groups of pure function fields, Proc. Japan Acad. 64 (1988), 170-173; corrigendum, ibid. 75 (1999), 22.
- K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257-258.
- I. Kimura, On class numbers of quadratic extensions over function fields, Manuscripta Math. 97 (1998), 81-91.
- T. Nagell, Über die Klassenzahl imaginär-quadratischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 1 (1922), 140-150.
- P. Roquette and H. Zassenhaus, A class rank estimate for algebraic number fields, J. London Math. Soc. 44 (1969), 31-38.
- M. Rosen, The Hilbert class fields in function fields, Exposition. Math. 5 (1987), 365-378.
- D. Shanks, The simplest cubic fields, Math. Comp. 28 (1974), 1137-1157.
- Y. Yamamoto, On unramified Galois extensions of quadratic number fields, Osaka J. Math. 7 (1970), 57-76.