Sharp Bounds for Symmetric and Asymmetric Diophantine Approximation
Sharp Bounds for Symmetric and Asymmetric Diophantine Approximation
摘要
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.
二级参考文献4
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1[1]Tong, J., Symmetric and asymmetric Diophantine approximation of continued fractions, Bull. Soc.Math. France, 117(1989), 59-67.
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3[3]Tong, J., Diophantine approximation of a single irrational number, J. Number Theory, 35(1990), 53-57.
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4[4]Tong, J., The conjugate property for Diophantine approximation of continued fractions, Proc. Amer.Math. Soc., 105(1989), 535-539.
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