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arXiv:1710.08990 [math.NT]AbstractReferencesReviewsResources

Quadratic Irrationals, Generating Functions, and Lévy Constants

Anna Belova, Peter Hazard

Published 2017-10-24Version 1

We show that the generating function corresponding to the sequence of denominators of the best rational approximants of a quadratic irrational is a rational function with integer coefficients. Consequently we can compute the L\'evy constant of any quadratic irrational explicitly in terms of its partial quotients.

Comments: 27 pages
Categories: math.NT, math.CO, math.DS
Subjects: 11J70, 11K50, 05A15
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