Abstract
In the 1950's Hasse gave a formula that relates the class number of a biquadratic dicyclic number field to the class numbers of its, three quadratic subfields. Similar formulas are derived here for biquadratic dicyclic extensions of more general base fields, in cases where the base fields retain several properties of ℚ.
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Berger, R.I.: Quadratic extensions with elementary abelianK 2(O). J. Algebra142, 394–404 (1991)
Conner, P.E. and Hurrelbrink, J.: Class number partity. Pure Math. Series8, World Scientific Publishing Co., Singapore (1988)
Dirichlet, G.L.: Recherches sur les formes quadratiques a coefficients et a indeterminees complexes. J. reine angew. Math.24, 291–371 (1842). (Werke 1, 411–496)
Hasse, H.: Über die Klassenzahl abelscher Zahlkörper.Akademie Verlag, Berlin (1952)
Herglotz, G.: Über einen Dirichletchen Satz. Math. Z.12, 255–261 (1922)
Hilbert, D.: Über den Dirichletschen biquadratischen Zahlkörper. Math. Annalen45, 309–340 (1894)
Hirabayashi, H. and Yoshino, K.: Remarks on unit indices of imaginary abelian number fields. Manuscripta math.60, 423–436 (1988)
Kubota, T.: Über die Beziehungen der Klassenzahlen der Unterkörper des bizyklischen biquadratischen Zahlkörpers. Nagoya Math. J.6, 119–127 (1953)
Kubota, T.: Über den bizyklischen biquadratischen Zahlkörper. Nagoya Math. J.10, 65–85 (1956)
Kuroda, S.: Über den Dirichletschen Körper. J. Fac. Sci. Imp. Univ. Tokyo, Sec. I, Vol. IV, Part 5, 383–406 (1943).
Kuroda, S.: Über die Klassenzahlen algebraischer Zahlkörper. Nagoya Math. J.1, 1–10 (1950)
Lang, S.: Algebraic Number Theory. Addison Wesley, Mass. (1970)
Washington, L.: Introduction to cyclotomic fields. Springer Verlag (1982)
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Berger, R.I. Hasse's class number product formula for generalized Dirichlet fields and other types of number fields. Manuscripta Math 76, 397–406 (1992). https://doi.org/10.1007/BF02567768
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DOI: https://doi.org/10.1007/BF02567768