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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Mollin, R.A. 1994. Use of the rabinowitsch polynomial to determine the class groups of a real quadratic field. Bulletin of the Australian Mathematical Society, Vol. 50, Issue. 03, p. 435.
    Louboutin, Stéphane 1993. Minorations d’unités fondamentales—applications. Nagoya Mathematical Journal, Vol. 130, Issue. , p. 1.
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On determining certain real quadratic fields with class number one and relating this property to continued fractions and primality properties

  • Eugène Dubois (a1) and Claude Levesque (a2)
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Thanks to K. Heegner [He], A. Baker [Ba] and H. Stark [S], we know that there are nine imaginary quadratic fields of class number one. Gauss conjectured that there are infinitely many real quadratic fields of class number one, but the conjecture is still open.

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COPYRIGHT: © Editorial Board of Nagoya Mathematical Journal 1991
References
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[Ba] Baker, A., Linear forms in the logarithms of algebraic numbers, Mathematica, 13 (1966), 204–216.
[Bel] Bernstein, L., Fundamental units and cycles in the period of real quadratic number fields, I, Pacific J. Math., 63, N°l, (1976), 37–61; J. Number Theory, 8 (1976), 446–491.
[Be2] Bernstein, L., Fundamental units and cycles in the period of real quadratic number fields, II, Pacific J. Math., 63, N°2, (1976), 63–78.
[H-K] Halter-Koch, F., Einige periodische Kettenbruchentwicklungen und Grundein-heiten quadratischer ordnungen, Abh. Math. Sem. Univ. Hamburg, 59 (1989), 157–169.
[He] Heegner, K., Diophantische Analysis und Modulfunktionen, Math. Z. 56 (1952), 227–253.
[Ho] Hoffstein, J., On the Siegel-Tatuzawa theorem, Acta Arith., 38 (1980), 167–174.
[Le] Levesque, C, Continued fraction expansions and fundamental units, J. Math. Phy. Sci., 22, N°l, (1988), 11–44.
[Le-R] Levesque, C. and Rhin, G., A few classes of periodic continued fractions, Utilitas Mathematica, 30 (1986), 79–107.
[Lo1] Louboutin, S., Arithmétique des corps quadratiques réels et fractions continues, Thèse de doctorat, Univ. Paris 7, Juin 1987.
[Lo2] Louboutin, S., Continued fractions and real quadratic fields, J. Number Theory, 30, N°2, (1988), 167–176.
[Lu] Lu, H., On the class number of real quadratic fields, Scientia Sinica, 2 (1979), 118–130.
[M1] Mollin, R. A., On the insolubility of a class of diophantine equations and the nontriviality of the class numbers of related real quadratic fields of Richaud-Degert type, Nagoya Math. J., 105 (1987), 39–47.
[M2] Mollin, R. A., On prime valued polynomials and class numbers of real quadratic fields, Nagoya Math. J., 112 (1988).
[M3] Mollin, R. A., Class numbers of quadratic fields determined by solvability of diophan tine equations, Math. Comp., 48, N° 177 (1987), 233–242.
[M-W] Mollin, R. A. and Williams, H. C., Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type (with one possible exception), from Number Theory, Proceedings (1990) edited by Mollin, R. A., published by W de G.
[N] Nyberg, M., Culminating and almost culminating continued fractions, Norsk. Mat. Tidsskr., 31 (1949), 95–99, (in Norwegian), MR A56–16.
[S] Stark, H. M., A complete determination of the complex quadratic fields of class number one, Michigan Math. J., 14 (1967), 1–27.
[T] Tatuzawa, T., On a theorem of Siegel, Japan J. Math., 21 (1951), 163–178.
[W] Williams, H. C., A note on the period length of the continued fraction expansion of certain , Utilitas Mathematica, 28 (1985), 201–209.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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