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On Yamamoto's reciprocity law

Author: Kenneth S. Williams
Journal: Proc. Amer. Math. Soc. 111 (1991), 607-609
MSC: Primary 11A15; Secondary 11R11, 11R29
MathSciNet review: 1047009
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Abstract: A simple proof of Yamamoto's reciprocity law is given.

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  • [1] Ezra Brown, Class numbers of quadratic fields, Symposia Mathematica, Vol. XV (Convegno di Strutture in Corpi Algebrici, INDAM, Rome, 1973) Academic Press, London, 1975, pp. 403–411. MR 0382226
  • [2] J. Bucher, Neues über die Pell’sche Gleichung, Mitt. Naturforsch. Ges. Luzern 14 (1943), 1–18 (German). MR 0021551
  • [3] P.G.L. Dirichlet, Einige neue Sätze über unbestimmte Gleichungen, Abh. Königlich Preussischen Akad. Wiss. 1834, pp. 649-664.
  • [4] Pierre Kaplan, Divisibilité par 8 du nombre des classes des corps quadratiques dont le 2-groupe des classes est cyclique, et réciprocité biquadratique, J. Math. Soc. Japan 25 (1973), 596–608 (French). MR 0323757,
  • [5] Yoshihiko Yamamoto, Congruences modulo 2ⁱ (𝑖=3,4) for the class numbers of quadratic fields, Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata, 1986) Nagoya Univ., Nagoya, 1986, pp. 205–215. MR 891897

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Keywords: Reciprocity, quadratic fields, classnumber
Article copyright: © Copyright 1991 American Mathematical Society