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

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

2009-12-06

arxiv.org/abs/0912.1039v1

Ramanujan J. 25 (3) (2011), 359-367

Mathematics

Number Theory

8 pages

Scientific paper

10.1007/s11139-011-9307-0

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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