Sharp Bounds for Symmetric and Asymmetric Diophantine Approximation |
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Authors: | Cornelis KRAAIKAMP and Ionica SMEETS |
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Affiliation: | [1]Delft University of Technology and Thomas Stieltjes Institute for Mathematics, EWI, DIAM, Mekelweg 4, 2628 CD Delft, Netherlands [2]Universiteit Leiden and Thomas Stieltjes Institute for Mathematics, Niels Bohrweg 1, 2333 CA Leiden |
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Abstract: | In 2004, Tong found bounds for the approximation quality of a regular continued fraction convergent to a rational number, expressed in bounds for both the previous and next approximation. The authors sharpen his results with a geometric method and give both sharp upper and lower bounds. The asymptotic frequencies that these bounds occur are also calculated. |
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Keywords: | Continued fractions Diophantine approximation Upper and lower bounds |
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