Sharp bounds for symmetric and asymmetric diophantine approximation

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.

Keywords

Continued fractions / Diophantine approximation / Upper and lower bounds

References

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