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.

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Correspondence to Cornelis Kraaikamp.

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Kraaikamp, C., Smeets, I. Sharp bounds for symmetric and asymmetric diophantine approximation. Chin. Ann. Math. Ser. B 32, 303–320 (2011). https://doi.org/10.1007/s11401-011-0629-4

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Keywords

  • Continued fractions
  • Diophantine approximation
  • Upper and lower bounds

2000 MR Subject Classification

  • 28D05
  • 11K50