Sharp bounds for symmetric and asymmetric Diophantine approximation

Details Sharp bounds for symmetric and asymmetric Diophantine approximation Sharp bounds for symmetric and asymmetric Diophantine approximation

2008-06-09

arxiv.org/abs/0806.1457v2

Mathematics

Number Theory

16 pages, 5 figures

Scientific paper

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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