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arXiv · 0708.3257

Tong's spectrum for Rosen continued fractions

Cor Kraaikamp·Thomas A. Schmidt·Ionica Smeets
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Abstract

The Rosen fractions are an infinite set of continued fraction algorithms, each giving expansions of real numbers in terms of certain algebraic integers. For each, we give a best possible upper bound for the minimum in appropriate consecutive blocks of approximation coefficients (in the sense of Diophantine approximation by continued fraction convergents). We also obtain metrical results for large blocks of ``bad'' approximations.

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Cor Kraaikamp, Thomas A. Schmidt, Ionica Smeets. 2007-08-23. Tong's spectrum for Rosen continued fractions. https://arxiv.org/abs/0708.3257

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