Comptes Rendus. Mathématique (Nov 2024)

Some lacunarity properties of partial quotients of real numbers

  • Zhao, Xuan,
  • Zhang, Zhenliang

DOI
https://doi.org/10.5802/crmath.594
Journal volume & issue
Vol. 362, no. G10
pp. 1089 – 1095

Abstract

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We consider lacunarity properties of sequence of partial quotients for real numbers in their continued fraction expansions. Hausdorff dimension of the sets of points with different lacunarity conditions on their partial quotients are calculated.

Keywords