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arXiv · 0912.1039

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

Giedrius Alkauskas
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Abstract

This paper continues investigations on the 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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Giedrius Alkauskas. 2009-12-06. Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function. https://doi.org/10.1007/s11139-011-9307-0

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