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Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function

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Abstract

This paper continues investigations on various integral transforms of the Minkowski question mark function. In this work we finally establish the long-sought formula for the moments, which does not explicitly involve regular continued fractions, though it has a hidden nice interpretation in terms of semi-regular continued fractions. The proof is self-contained and does not rely on previous results by the author.

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Authors and Affiliations

  1. Institute of Mathematics, Department of Integrative Biology, Universität für Bodenkultur Wien, Gregor Mendel-Straße 33, 1180, Vienna, Austria

    Giedrius Alkauskas

  2. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225, Vilnius, Lithuania

    Giedrius Alkauskas

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  1. Giedrius Alkauskas
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Correspondence to Giedrius Alkauskas.

Additional information

The author gratefully acknowledges support from the Austrian Science Fund (FWF) under the project Nr. P20847-N18.

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Alkauskas, G. Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function. Ramanujan J 25, 359–367 (2011). https://doi.org/10.1007/s11139-011-9307-0

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  • DOI: https://doi.org/10.1007/s11139-011-9307-0

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