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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1047009-X
MathSciNet review: 1047009
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Abstract: A simple proof of Yamamoto's reciprocity law is given.


References [Enhancements On Off] (What's this?)

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  • [2] J. Bucher, Neues über die Pell'sche Gleichung, Mitt. Naturforsch. Ges. Luzern 14 (1943), 1-18. MR 0021551 (9:78e)
  • [3] P.G.L. Dirichlet, Einige neue Sätze über unbestimmte Gleichungen, Abh. Königlich Preussischen Akad. Wiss. 1834, pp. 649-664.
  • [4] P. 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. MR 0323757 (48:2113)
  • [5] Y. Yamamoto, Congruences modulo $ {2^i}(i = 3,4)$ for the class numbers of quadratic fields, Proc. Internat. Conf. on Class Numbers and Fundamental Units of Algebraic Number Fields, Katata, Japan, June 24-28, 1986, pp. 205-215. MR 891897 (88k:11074)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1047009-X
Keywords: Reciprocity, quadratic fields, classnumber
Article copyright: © Copyright 1991 American Mathematical Society

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