Length of continued fractions in principal quadratic fields
Guillaume Grisel
Acta Arithmetica, Tome 84 (1998), p. 35-49 / Harvested from The Polish Digital Mathematics Library
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Let d ≥ 2 be a square-free integer and for all n ≥ 0, let l((√d)2n+1) be the length of the continued fraction expansion of (√d)2n+1. If ℚ(√d) is a principal quadratic field, then under a condition on the fundamental unit of ℤ[√d] we prove that there exist constants C₁ and C₂ such that C₁(√d)2n+1≥l((√d)2n+1)≥C₂(√d)2n+1 for all large n. This is a generalization of a theorem of S. Chowla and S. S. Pillai [2] and an improvement in a particular case of a theorem of [6].

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207153 
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Guillaume Grisel. Length of continued fractions in principal quadratic fields. Acta Arithmetica, Tome 84 (1998) pp. 35-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav85i1p35bwm/

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