Quadratic function fields whose class numbers are not divisible by three

• Autorzy: Humio Ichimura
• Języki publikacji: EN

Kategorie tematyczne

• 11R11: Quadratic extensions
• 11R29: Class numbers, class groups, discriminants
• 11R58: Arithmetic theory of algebraic function fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 91
• Numer: 2
• Strony: 181-190

Daty

wydano

1999

otrzymano

1999-02-12

Twórcy

autor

Humio Ichimura

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

Bibliografia

• [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.