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

Florin P. Boca, Christopher Linden

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)35-57
Number of pages23
JournalMonatshefte fur Mathematik
Volume187
Issue number1
DOIs
Publication statusPublished - Sep 1 2018

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Keywords

  • Even continued fraction
  • Farey map
  • Gauss map
  • Hölder exponent
  • Odd continued fraction
  • Question mark function

ASJC Scopus subject areas

  • Mathematics(all)

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