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NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS

  • YASUHIRO KISHI (a1)

Abstract

We prove that the class number of the imaginary quadratic field is divisible by n for any positive integers k and n with 22k < 3n, by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.

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References

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1.Ankeny, N. C. and Chowla, S., On the divisibility of the class number of quadratic fields, Pacific J. Math. 5 (1955), 321324.
2.Bugeaud, Y. and Shorey, T. N., On the number of solutions of the generalized Ramanujan-Nagell equation, J. Reine Angew. Math. 539 (2001), 5574.
3.Gross, B. H. and Rohrlich, D. E., Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), 201224.
4.Herschfeld, A., The equation 2x − 3y = d, Bull. Amer. Math. Soc. 42 (1936), 231234.
5.Ichimura, H., Note on the class numbers of certain real quadratic fields, Abh. Math. Sem. Univ. Hamburg 73 (2003), 281288.
6.Mollin, R. A., Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields, Glasgow Math. J. 38 (1996), 195197.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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