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Remark on the divisibility of the class numbers of certain quartic number fields by $ 5$

Author: Akira Endô
Journal: Proc. Amer. Math. Soc. 91 (1984), 513-517
MSC: Primary 11R29; Secondary 11R16
MathSciNet review: 746079
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Abstract: The congruence relation modulo 5 between the class numbers of the real and imaginary quartic subfields of the extension of a quadratic number field obtained by adjoining a fifth root of unity is studied.

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  • [1] H. Hasse, Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörpern, Abh. Deutsch. Akad. Wiss. Berlin (Math.-Nat.) 1948 (1950), 95 pp. MR 0033863 (11:503d)
  • [2] T. Kubota, Über den bizyklischen biquadratischen Zahlkörper, Nagoya Math. J. 10 (1956), 65-85. MR 0083009 (18:643e)
  • [3] A. Kudo, On the class number relation of imaginary abelian fields, J. Math. Soc. Japan 27 (1975), 150-159. MR 0360520 (50:12968)
  • [4] S. Kuroda, Über den Dirichletschen Körper, J. Fac. Sci. Imp. Univ. Tokyo Sect. I 4 (1943), 383-406. MR 0021031 (9:12f)
  • [5] -, Über die Klassenzahlen algebraischer Zahlkörper, Nagoya Math. J. 1 (1950), 1-10.
  • [6] C. J. Parry, Real quadratic fields with class numbers divisible by five, Math. Comp. 31 (1977), 1019-1029. MR 0498483 (58:16593)
  • [7] -, On the class number of relative quadratic fields, Math. Comp. 32 (1978), 1261-1270. MR 502013 (80h:12004)

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Keywords: Quartic number field, class number, $ p$-adic $ L$-function
Article copyright: © Copyright 1984 American Mathematical Society

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