Sharp bounds for symmetric and asymmetric Diophantine approximation

Cor Kraaikamp; Ionica Smeets

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arXiv · 0806.1457

Sharp bounds for symmetric and asymmetric Diophantine approximation

Cor Kraaikamp·Ionica Smeets

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Abstract

In 2004, J.C. Tong found bounds for the approximation quality of a regular continued fraction convergent of a rational number, expressed in bounds for both the previous and next approximation. We sharpen his results with a geometric method and give both sharp upper and lower bounds. We also calculate the asymptotic frequency that these bounds occur.

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Cor Kraaikamp, Ionica Smeets. 2009-08-25. Sharp bounds for symmetric and asymmetric Diophantine approximation. https://arxiv.org/abs/0806.1457

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