Hausdorff Dimension of the Exceptional Set in Engel Continued Fractions

Mei Ying LÜ, Jing XIE

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (6) : 1003-1008.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (6) : 1003-1008. DOI: 10.12386/A20210058

Hausdorff Dimension of the Exceptional Set in Engel Continued Fractions

  • Mei Ying LÜ, Jing XIE
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Abstract

For any real number x∈(0,1), there exists a unique Engel continued fractions of x. In this paper, we mainly discuss the exceptional set which the logarithms of the partial quotients grow with non-linear rate. We completely characterize the Hausdorff dimension of the relevant exceptional set.

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Engel continued fractions / exceptional sets / Hausdorff dimensions

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Mei Ying LÜ, Jing XIE. Hausdorff Dimension of the Exceptional Set in Engel Continued Fractions. Acta Mathematica Sinica, Chinese Series, 2022, 65(6): 1003-1008 https://doi.org/10.12386/A20210058

References

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