Quadratic Irrationals, Generating Functions, and L\'evy Constants
Number Theory
2018-05-03 v2 Combinatorics
Dynamical Systems
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.
Cite
@article{arxiv.1710.08990,
title = {Quadratic Irrationals, Generating Functions, and L\'evy Constants},
author = {Anna Belova and Peter Hazard},
journal= {arXiv preprint arXiv:1710.08990},
year = {2018}
}
Comments
Section 1 (Introduction) and Section 3 rewritten. Some minor corrections. 5 figures added. 29 pages