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Estimate for dispersion of lengths of continued fractions

Abstract

An estimate for dispersion of lengths of continued fractions is proved for fixed denominator. This estimate improves the trivial one by the logarithm of the denominator.

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Correspondence to V. A. Bykovskii.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 15–26, 2005.

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Bykovskii, V.A. Estimate for dispersion of lengths of continued fractions. J Math Sci 146, 5634–5643 (2007). https://doi.org/10.1007/s10958-007-0378-9

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Keywords

  • Positive Integer
  • Prime Number
  • Asymptotic Formula
  • Continue Fraction
  • Fibonacci Sequence