Structure of the Markoff spectrum below √12

Richard Bumby

Displaying similar documents to “Structure of the Markoff spectrum below √12”

Limit points in the Lagrange spectrum of a quadratic field

S.M.J. Wilson (1980)

Bulletin de la Société Mathématique de France

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Halfway to a solution of $X^{2} - D Y^{2} = - 3$

R. A. Mollin, A. J. Van der Poorten, H. C. Williams (1994)

Journal de théorie des nombres de Bordeaux

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It is well known that the continued fraction expansion of $\sqrt{D}$ readily displays the midpoint of the principal cycle of ideals, that is, the point halfway to a solution of $x^{2} - D y^{2} = \pm 1$ . Here we notice that, analogously, the point halfway to a solution of $x^{2} - D y^{2} = - 3$ can be recognised. We explain what is going on.