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11-XX Number theory
11Rxx Algebraic number theory: global fields
11R11 Quadratic extensions

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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

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.

Hermite's constant for quadratic number fields.

Baeza, Ricardo, Coulangeon, Renaud, Icaza, Maria Ines, O'Ryan, Manuel (2001)

Experimental Mathematics

Hilbert Modular Surfaces and the Classification of Algebraic Surfaces.

F. Hirzebruch, A. de Van de Ven (1974)

Inventiones mathematicae

Hyperbolic tessellations, modular symbols, and elliptic curves over complex quadratic fields

J. E. Cremona (1984)

Compositio Mathematica

Currently displaying 1 – 4 of 4