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

Abstract

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

arXiv comment11 pages, 1 figure (final version). Lithuanian Math. J. (to appear)

References in corpus (3)

• The Minkowski question mark function: explicit series for the dyadic period function and moments
• The moments of Minkowski question mark function: the dyadic period function
• Generating and zeta functions, structure, spectral and analytic properties of the moments of Minkowski question mark function

Cited by in corpus (6)

• The Minkowski question mark function: explicit series for the dyadic period function and moments
• The moments of Minkowski question mark function: the dyadic period function
• Generating and zeta functions, structure, spectral and analytic properties of the moments of Minkowski question mark function
• Orthogonal polynomials for Minkowski's question mark function
• Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function
• Fourier-Stieltjes coefficients of the Minkowski question mark function