Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one

• Autorzy: Stéphane Louboutin , Ryotaro Okazaki
• Języki publikacji: EN

Kategorie tematyczne

• 11R11: Quadratic extensions
• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1994
• Tom: 67
• Numer: 1
• Strony: 47-62

Daty

wydano

1994

otrzymano

1993-04-27

poprawiono

1993-10-05

Twórcy

autor

Stéphane Louboutin

• Université de Caen, U.F.R. Sciences, Département de Mathématiques, Esplanade de La Paix, 14032 Caen Cedex, France

autor

Ryotaro Okazaki

• Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-01, Japan

Bibliografia

• [H] J. Hoffstein, Some analytic bounds for zeta functions and class numbers, Invent. Math. 55 (1979), 37-47.
• [Kub] T. Kubota, Über die Beziehung der Klassenzahlen der Unterkörper des bizyklischen biquadratischen Zahlkörper, Nagoya Math. J. 6 (1953), 119-127.
• [Lou 1] S. Louboutin, On the class number one problem for non-normal quartic CM-fields, Tôhoku Math. J., to appear.
• [Lou 2] S. Louboutin, Calcul du nombre de classes des corps de nombres, preprint, 1992.
• [Lou 3] S. Louboutin, Calcul des nombres de classes relatifs. Application aux corps octiques quaternioniques à multiplication complexe, C. R. Acad. Sci. Paris Sér. I 317 (1993), 643-646.
• [Lou 4] S. Louboutin, Determination of all quaternion octic CM-fields with class number 2, preprint, 1993.
• [O] A. M. Odlyzko, Some analytic estimates of class numbers and discriminants, Invent. Math. 29 (1975), 275-286.
• [Ok] R. Okazaki, On evaluation of L-functions over real quadratic fields, J. Math. Kyoto Univ. 31 (1991), 1125-1153.
• [Se] J. P. Serre, Corps Locaux, Hermann, 1968.
• [W] L. C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Math. 83, Springer, 1982.
• [Y] K. Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp., to appear.