Subexponentially increasing sums of partial quotients in continued fraction expansions

DOI10.1017/S0305004115000742zbMath1371.11123arXiv1405.4747OpenAlexW1820287612MaRDI QIDQ5360378

Michał Rams, Lingmin Liao

Publication date: 28 September 2017

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

Full work available at URL: https://arxiv.org/abs/1405.4747

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Hausdorff and packing measures (28A78) Metric theory of continued fractions (11K50)

Related Items (18)

Upper and lower fast Khintchine spectra in continued fractions ⋮ Big Birkhoff sums in $d$-decaying Gauss like iterated function systems ⋮ Hausdorff dimension of certain sets arising in Engel continued fractions ⋮ 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 ⋮ On sums of partial quotients in Hurwitz continued fraction expansions ⋮ ON LÜROTH EXPANSIONS IN WHICH THE LARGEST DIGIT GROWS WITH SLOWLY INCREASING SPEED ⋮ A remark on big Birkhoff sums in \(d\)-decaying Gauss like iterated function systems ⋮ On the digits of Schneider's \(p\)-adic 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 ⋮ Large deviation principle for arithmetic functions in continued fraction expansion ⋮ MULTIFRACTAL ANALYSIS OF THE BIRKHOFF SUMS OF SAINT-PETERSBURG POTENTIAL ⋮ Some exceptional sets of Borel-Bernstein theorem in continued fractions ⋮ Limit theorems for sums of products of consecutive partial quotients of continued fractions ⋮ ON THE LARGEST PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS

Cites Work

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• Limit theorems for sums of partial quotients of continued fractions
• On the distribution for sums of partial quotients in continued fraction expansions
• On sums of partial quotients in continued fraction expansions
• The distribution of the largest digit in continued fraction expansions
• On Khintchine exponents and Lyapunov exponents of continued fractions
• A conjecture of Erdös on continued fractions
• Increasing digit subsystems of infinite iterated function systems
• Multifractal analysis of Birkhoff averages for countable Markov maps

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