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Journal of Mathematical Sciences

, Volume 234, Issue 5, pp 595–597 | Cite as

Alternating Sums of Elements of Continued Fractions and the Minkowski Question Mark Function

  • E. P. Golubeva
Article
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The paper considers the function A(t) (0 ≤ t ≤ 1), related to the distribution of alternating sums of elements of continued fractions. The function A(t) possesses many properties similar to those of the Minkowski function ?(t). In particular, A(t) is continuous, satisfies similar functional equations, and A′(t) = 0 almost everywhere with respect to the Lebesgue measure. However, unlike ?(t), the function A(t) is not monotonically increasing. Moreover, on any subinterval of [1, 0], it has a sharp extremum.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The Bonch-Bruevich St. Petersburg State University of TelecommunicationsSt. PetersburgRussia

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