O Fareyových zlomcích
Odvození vzorce pro součet kladných a celistvých mocnin čísel přirozené řady ve formě nezávislé
On an additive property of squares and primes
On consecutive Farey arcs
On consecutive Farey arcs II
On sums of powers of the positive integers
The pairs (k,m) are studied such that for every positive integer n we have .
On the distribution of the free path length of the linear flow in a honeycomb
Consider the region obtained by removing from the discs of radius , centered at the points of integer coordinates with . We are interested in the distribution of the free path length (exit time) of a point particle, moving from along a linear trajectory of direction , as . For every integer number , we prove the weak convergence of the probability measures associated with the random variables , explicitly computing the limiting distribution. For , respectively , this result leads...
On the Farey fractions with denominators in arithmetic progression.
On the metric theory of continued fractions
On uniform distribution of sequences
Orderings of the rationals and dynamical systems
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...