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.
 Publication:

arXiv eprints
 Pub Date:
 February 2008
 arXiv:
 arXiv:0802.2721
 Bibcode:
 2008arXiv0802.2721A
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Classical Analysis and ODEs;
 11A55;
 26A30;
 41A60
 EPrint:
 11 pages, 1 figure (final version). Lithuanian Math. J. (to appear)