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On Minkowski type question mark functions associated with even or odd continued fractions

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Abstract

We study analogues of Minkowski’s question mark function ?(x) related to continued fractions with even or with odd partial quotients. We prove that these functions are Hölder continuous with precise exponents, and that they linearize the appropriate versions of the Gauss and Farey maps.

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Acknowledgements

We are grateful to the referees for their valuable input that contributed to a number of clarifications and improved the presentation of the paper. Florin P. Boca would like to acknowledge partial support during his visits to IMAR Bucharest by a grant from Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, Project PN-III-P4-ID-PCE-2016-0823, within PNCDI III.

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  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Florin P. Boca & Christopher Linden

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  1. Florin P. Boca
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  2. Christopher Linden
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Correspondence to Florin P. Boca.

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Communicated by A. Constantin.

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Boca, F.P., Linden, C. On Minkowski type question mark functions associated with even or odd continued fractions. Monatsh Math 187, 35–57 (2018). https://doi.org/10.1007/s00605-018-1205-8

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