A new upper bound on the star discrepancy of -sequences.
A note on simultaneous Diophantine approximation in positive characteristic
A note on the approximation by continued fractions under an extra condition.
A note on the figure of merit of 2-dimensional rank 2 lattice rules.
A note on the Hausdorff-Besicovitch dimension of systems of linear forms
A note on the pseudorandomness of the Liouville function
A Note on the Voronoi Summation Formula.
A note on the weighted Khintchine-Groshev Theorem
Let denote the set of –approximable points in . The classical Khintchine–Groshev theorem assumes a monotonicity condition on the approximating functions . Removing monotonicity from the Khintchine–Groshev theorem is attributed to different authors for different cases of and . It can not be removed for as Duffin–Schaeffer provided the counter example. We deal with the only remaining case and thereby remove all unnecessary conditions from the Khintchine–Groshev theorem.
A note on zero-one laws in metrical Diophantine approximation
A notion of diaphony based on p-adic arithmetic
A numerical sampling problem and the Weyl pseudorandom numbers.
A -adic study of the partial sums of the harmonic series.
A partition of the unit sphere into regions of equal area and small diameter.
A probabilistic setting for prime number theory
A problem of Erdős-Szüsz-Turán on diophantine approximation
A problem of Galambos on Engel expansions
1. Introduction. Given x in (0,1], let x = [d₁(x),d₂(x),...] denote the Engel expansion of x, that is, (1) , where is a sequence of positive integers satisfying d₁(x) ≥ 2 and for j ≥ 1. (See [3].) In [3], János Galambos proved that for almost all x ∈ (0,1], (2) He conjectured ([3], P132) that the Hausdorff dimension of the set where (2) fails is one. In this paper, we prove this conjecture: Theorem. . We use L¹ to denote the one-dimensional Lebesgue measure on (0,1] and to denote the Hausdorff...
A propos du théorème de Cassels-Schmidt concernant de nombres normaux
A self-similar tiling generated by the minimal Pisot number
A sequence adapted from the movement of the center of mass of two planets in solar system
In this paper we derive a sequence from a movement of center of~mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.
A Sequence Has Almost Nowhere Small Discrepancy.