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

TL;DR

This paper derives an asymptotic formula for the moments of Minkowski's question mark function, revealing insights into the distribution of rationals in the Farey tree using a variation of the Laplace method.

Contribution

It introduces a novel application of a Laplace method variation to obtain asymptotic formulas for the moments of Minkowski's question mark function.

Findings

Established the asymptotic behavior of the moments

Demonstrated the applicability of a modified Laplace method

Enhanced understanding of the distribution of rationals in Farey sequences

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.