PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2000 | 92 | 4 | 319-338
Tytuł artykułu

Inclusion of CM-fields and divisibility ofrelative class numbers

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
92
Numer
4
Strony
319-338
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-06-03
poprawiono
1999-05-17
Twórcy
  • Doshisha University, Department of Mathematics, Faculty of Engineering, Kyotanabe, Kyoto, 610-0321 Japan
Bibliografia
  • [1] S. Arno, The imaginary quadratic fields of class number 4, Acta Arith. 60 (1992), 321-334.
  • [2] A. Baker, A remark on the class number of quadratic fields, Bull. London Math. Soc. 1 (1966), 98-102.
  • [3] A. Baker, Imaginary quadratic fields with class number 2, Ann. of Math. 94 (1971), 139-152.
  • [4] H. Furuya, On divisibility by 2 of the relative class numbers of imaginary number fields, Tôhoku Math. J. 23 (1971), 207-218.
  • [5] D. M. Goldfeld, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer, Ann. Scuola Norm. Sup. Pisa (4) 3 (1976), 623-663.
  • [6] B. Gross et D. Zagier, Points de Heegner et derivées de fonctions L, C. R. Acad. Sci. Paris 297 (1983), 85-87.
  • [7] K. Győry, Sur une classe des corps de nombres algébriques et ses applications, Publ. Math. Debrecen 22 (1975), 151-175.
  • [8] K. Heegner, Diophantische Analysis und Modulfunktionen, Math. Z. 56 (1952), 227-253.
  • [9] H. Heilbronn, On real zeros of Dedekind ζ-functions, Canad. J. Math. 25 (1973), 870-873.
  • [10] M. Hirabayashi and K. Yoshino, Remarks on unit indices of imaginary abelian number fields II, Manuscripta Math. 64 (1989), 235-251.
  • [11] J. Hoffstein, Some analytic bounds for zeta functions and class numbers, Invent. Math. 55 (1979), 37-47.
  • [12] K. Horie, On a ratio between relative class numbers, Math. Z. 211 (1992), 505-521.
  • [13] K. Horie, On CM-fields with the same maximal real subfield, Acta Arith. 67 (1994), 219-227.
  • [14] D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp. 24 (1970), 433-451.
  • [15] F. Lemmermeyer, Kuroda's class number formula, Acta Arith. 66 (1994), 245-260.
  • [16] F. Lemmermeyer, Ideal class groups of cyclotomic number fields I, ibid. 72 (1995), 347-359.
  • [17] F. Lemmermeyer, On 2-class field towers of some imaginary quadratic number fields, Abh. Math. Sem. Univ. Hamburg 67 (1997), 205-214.
  • [18] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arith. 14 (1968), 117-140.
  • [19] H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, ibid. 24 (1974), 529-542.
  • [20] P. Roquette, On class field towers, in: Algebraic Number Theory, J. W. S. Cassels and A. Fröhlich (eds.), Academic Press, London, 1967, 231-249.
  • [21] G. Shimura, Abelian Varieties with Complex Multiplication and Modular Functions, Princeton Univ. Press, Princeton, 1997.
  • [22] G. Shimura and Y. Taniyama, Complex Multiplication of Abelian Varieties, The Mathematical Society of Japan, 1961.
  • [23] H. M. Stark, A complete determination of the complex quadratic fields of class number one, Michigan Math. J. 14 (1967), 1-27.
  • [24] H. M. Stark, On complex quadratic fields with class number two, Math. Comp. 29 (1975), 289-302.
  • [25] H. M. Stark, Some effective cases of the Brauer-Siegel theorem, Invent. Math. 23 (1974), 135-152.
  • [26] T. Takagi, Über eine Theorie des relativ Abel'schen Zahlkörpers, in: T. Takagi, Collected Papers, Springer, Tokyo, 1990, 73-167.
  • [27] L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982, 2nd ed., 1991.
  • [28] E. E. Whitaker, A determination of the imaginary quadratic number fields with Klein-four group as class group, thesis, 1972.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav92i4p319bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.