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arXiv · 1710.08990

Quadratic Irrationals, Generating Functions, and L\'evy Constants

Anna Belova·Peter Hazard
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Abstract

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 a finite number of its convergents.

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Anna Belova, Peter Hazard. 2017-10-24. Quadratic Irrationals, Generating Functions, and L\'evy Constants. https://arxiv.org/abs/1710.08990

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