The distribution of the largest digit in continued fraction expansions

DOI10.1017/S0305004108001771zbMath1162.11042MaRDI QIDQ3598124

Jun Wu, Jian Xu

Publication date: 30 January 2009

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Continued fractions (11A55) Metric theory of continued fractions (11K50)

Related Items (20)

The relative growth rate of the largest digit in continued fraction expansions ⋮ METRIC THEORY OF PARTIAL QUOTIENTS OF N-CONTINUED FRACTIONS ⋮ ON THE INCREASING PARTIAL QUOTIENTS OF CONTINUED FRACTIONS OF POINTS IN THE PLANE ⋮ Exceptional sets related to the largest digits in Lüroth expansions ⋮ On the exceptional sets concerning the leading partial quotient in continued fractions ⋮ SOME RESULTS ON THE LARGEST PARTIAL QUOTIENT IN CONTINUED FRACTIONS ⋮ The distribution of the large partial quotients in continued fraction expansions ⋮ Level sets of partial maximal digits for Lüroth expansion ⋮ Slow increasing functions and the largest partial quotients in continued fraction expansions ⋮ ON LÜROTH EXPANSIONS IN WHICH THE LARGEST DIGIT GROWS WITH SLOWLY INCREASING SPEED ⋮ On sets of exact Diophantine approximation over the field of formal series ⋮ Chaotic and topological properties of continued fractions ⋮ Full dimensional sets of reals whose sums of partial quotients increase in certain speed ⋮ A remark on Liao and Rams' result on the distribution of the leading partial quotient with growing speed \(e^{n^{1/2}}\) in continued fractions ⋮ Subexponentially increasing sums of partial quotients in continued fraction expansions ⋮ The relative growth rate of the largest partial quotient to the sum of partial quotients in continued fraction expansions ⋮ A generalization of the Jarník–Besicovitch theorem by continued fractions ⋮ Some exceptional sets of Borel-Bernstein theorem in continued fractions ⋮ ON THE LARGEST DEGREE OF THE PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS OVER THE FIELD OF FORMAL LAURENT SERIES ⋮ ON THE LARGEST PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS

Cites Work

• A remark on the growth of the denominators of convergents
• Explicit continued fractions with expected partial quotient growth

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