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An asymptotic formula for the moments of the Minkowski question mark function in the interval [0, 1]

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Abstract

In this paper, we prove an asymptotic formula for the moments of the Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is to demonstrate that a certain variation of a Laplace method is applicable in this problem, and hence the task reduces to a number of technical calculations.

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References

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Authors and Affiliations

  1. The School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    G. Alkauskas

  2. The Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius, Lithuania

    G. Alkauskas

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  1. G. Alkauskas
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Correspondence to G. Alkauskas.

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Dedicated to Antanas Laurinčikas on the occasion of his 60th birthday

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Alkauskas, G. An asymptotic formula for the moments of the Minkowski question mark function in the interval [0, 1]. Lith Math J 48, 357–367 (2008). https://doi.org/10.1007/s10986-008-9027-3

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  • DOI: https://doi.org/10.1007/s10986-008-9027-3

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