Ideal class groups of cyclotomic number fields I

• Autorzy: Franz Lemmermeyer
• Języki publikacji: EN

Kategorie tematyczne

• 11R18: Cyclotomic extensions
• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 72
• Numer: 4
• Strony: 347-359

Daty

wydano

1995

otrzymano

1994-08-19

Twórcy

autor

Franz Lemmermeyer

• Erwin-Rohde-Str. 19, D-69120 Heidelberg, Germany

Bibliografia

• [F] B. Ferrero, The cyclotomic ℤ₂-extension of imaginary quadratic number fields, Amer. J. Math. 102 (1980), 447-459.
• [H] H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Springer, Berlin, 1985.
• [HY] M. Hirabayashi and K. Yoshino, Remarks on unit indices of imaginary abelian number fields, Manuscripta Math. 60 (1988), 423-436.
• [Ho] K. Horie, On a ratio between relative class numbers, Math. Z. 211 (1992), 505-521.
• [L] F. Lemmermeyer, Kuroda's class number formula, Acta Arith. 66 (1994), 245-260.
• [Lou] S. Louboutin, Determination of all quaternion octic CM-fields with class number 2, J. London Math. Soc., to appear.
• [LOO] S. Louboutin, R. Okazaki and M. Olivier, The class number one problem for some non-abelian normal CM-fields, preprint, 1994.
• [M] T. Metsänkylä, Über den ersten Faktor der Klassenzahl des Kreiskörpers, Ann. Acad. Sci. Fenn. Ser. A I 416, 1967.
• [MM] J. M. Masley and H. L. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256.
• [O] R. Okazaki, On evaluation of L-functions over real quadratic fields, J. Math. Kyoto Univ. 31 (1991), 1125-1153.
• [S] A. Scholz, Über die Lösbarkeit der Gleichung t² - Du² = -4, Math. Z. 39 (1934), 95-111.
• [U] K. Uchida, Imaginary quadratic number fields with class number one, Tôhoku Math. J. 24 (1972), 487-499.
• [W] L. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982.
• [We] J. Westlund, On the class number of the cyclotomic number field, Trans. Amer. Math. Soc. 4 (1903), 201-212.