Discrepancy of sums of three arithmetic progressions.
Discrepancy of symmetric products of hypergraphs.
Discrepancy of weighted matrix nets
Distribution de points sur une sphère
Distribution of roots of polynomial congruences.
Distribution of the power generator over a residue ring for parts of the period.
Duality for digital nets and its applications
Dyadic diaphony
Dyadic diaphony of digital sequences
The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital -sequences over , . These formulae show that for fixed , the dyadic diaphony has the same values for any digital -sequence. For , it follows that the dyadic diaphony and the diaphony of special digital -sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony of digital...
Effective polynomial upper bounds to perigees and numbers of (3x+d)-cycles of a given oddlength
Einige Diskrepanzabschätzungen für Punktfolgen im Rs.
Ensemble d'invariants pour les produits croisés de Anzai
Équidistribution presque partout modulo 1 de suites oscillantes perturbées
Equidistribution Properties of Nonlinear Congruential Pseudorandom Numbers.
Erdös-Turán Type Discrepancy Bounds.
Ergodicity of a class of cylinder flows related to irregularities of distribution
Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus
Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality
We prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma-Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. We also discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure...
GCD sums from Poisson integrals and systems of dilated functions
Upper bounds for GCD sums of the form are established, where is any sequence of distinct positive integers and ; the estimate for solves in particular a problem of Dyer and Harman from 1986, and the estimates are optimal except possibly for . The method of proof is based on identifying the sum as a certain Poisson integral on a polydisc; as a byproduct, estimates for the largest eigenvalues of the associated GCD matrices are also found. The bounds for such GCD sums are used to establish...
General discrepancy estimates II: the Haar function system