Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences
Comparing the distribution of (nα)-sequences
Construction of minimal bracketing covers for rectangles.
Constructions of digital nets
Constructions of digital nets using global function fields
Continued fractions, multidimensional diophantine approximations and applications
This paper is a brief review of some general Diophantine results, best approximations and their applications to the theory of uniform distribution.
Corrigendum to: "Improvements on the star discrepancy of (t,s)-sequences" (Acta Arith. 154 (2012), 61-78)
This short note is intended to correct an inaccuracy in the proof of Theorem 3 in the paper mentioned in the title. The result of Theorem 3 remains true without any other change in the proof. Furthermore, a misprint is pointed out.
Corrigendum to the paper "On the distribution of s-dimensional Kronecker sequences" Acta Arith. 51 (1988), 335-347
Digital expansion of exponential sequences
We consider the -ary digital expansion of the first terms of an exponential sequence . Using a result due to Kiss and Tichy [8], we prove that the average number of occurrences of an arbitrary digital block in the last digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first digits, where is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo ...
Digital Nets and Sequences Constructed over Finite Rings and Their Application to Quasi-Monte Carlo Integration.
Digital (t,m,s)-nets and the spectral test
Discrépance de suites associées à un système de numération (en dimension s)
Discrépance des suites de Farey
On étudie la discrépance absolue de la suite de Farey d’ordre et on montre, en utilisant notamment une majoration d’une intégrale portant sur la fonction sommatoire de la fonction de Möbius, qu’elle est égale à exactement, ce qui est la valeur locale au point d’abscisse .
Discrépance quadratique de la suite de van der Corput et de sa symétrique
Discrépances de suites associées à un système de numération (en dimension un)
Discrepancies of point sequences on the Sierpiński carpet
Discrepancy and diaphony of digital (0,1)-sequences in prime base
Discrepancy and integration in function spaces with dominating mixed smoothness [Book]
Discrepancy estimates for some linear generalized monomials
We consider sequences modulo one that are generated using a generalized polynomial over the real numbers. Such polynomials may also involve the integer part operation [·] additionally to addition and multiplication. A well studied example is the (nα) sequence defined by the monomial αx. Their most basic sister, , is less investigated. So far only the uniform distribution modulo one of these sequences is resolved. Completely new, however, are the discrepancy results proved in this paper. We show...
Discrepancy of cartesian products of arithmetic progressions.