- Journal Details
- Format
- Journal
- eISSN
- 2309-5377
- First Published
- 30 Dec 2013
- Publication timeframe
- 2 times per year
- Languages
- English

#### Search

#### Abstract

We intend to unroll the surprizing properties of the Thue-Morse sequence with a harmonic analysis point of view, and mention in passing some related open questions.

#### Keywords

- Thue-Morse
- Rudin-Shapiro
- sum of digits
- trigonometric polynomial
- correlation measure
- singular measure

- Open Access

Motzkin’s Maximal Density and Related Chromatic Numbers

Page range: 27 - 45

#### Abstract

This paper concerns the problem of determining or estimating the maximal upper density of the sets of nonnegative integers

#### Keywords

- maximal density
- generalized Fibonacci numbers
- fractional coloring
- circular coloring

#### MSC 2010

- 11B05
- 11B39

- Open Access

On the Discrepancy of Two Families of Permuted Van der Corput Sequences

Page range: 47 - 64

#### Abstract

A permuted van der Corput sequence

#### Keywords

- van der Corput sequence
- extreme discrepancy
- permutation
- permutation polynomial
- Carlitz rank

#### MSC 2010

- 11K38
- 11K06
- 11T06

- Open Access

Metrical Star Discrepancy Bounds for Lacunary Subsequences of Digital Kronecker-Sequences and Polynomial Tractability

Page range: 65 - 86

#### Abstract

The star discrepancy ^{d}^{−1}).

In 2001 it has been shown by Heinrich, Novak, Wasilkowski and Woźniakowski that for every integer ^{d}

Unfortunately the result by Heinrich et al. and also later variants thereof by other authors are pure existence results and until now no explicit construction of point sets with the above properties is known. Quite recently Löbbe studied lacunary subsequences of Kronecker’s (

In this paper we show a corresponding result for digital Kronecker sequences, which are a non-archimedean analog of classical Kronecker sequences.

#### Keywords

- star discrepancy
- digital Kronecker-sequence
- polynomial tractability
- quasi-Monte Carlo

#### MSC 2010

- 11K38
- 11K31
- 11K45

- Open Access

An Extension of the Digital Method Based on b -Adic Integers

Page range: 87 - 107

#### Abstract

We introduce a hybridization of digital sequences with uniformly distributed sequences in the domain of

#### Keywords

- quasi-Monte Carlo methods
- construction
- digital method
- digit expansion
- -adic integers

#### MSC 2010

- 11J71
- 11K16
- 11K38
- 11F85

- Open Access

Construction of Uniformly Distributed Linear Recurring Sequences Modulo Powers of 2

Page range: 109 - 129

#### Abstract

The aim of the present paper is to provide the background to construct linear recurring sequences with uniform distribution modulo 2^{s}

#### Keywords

- uniform distribution
- construction
- long period
- large numbers

#### MSC 2010

- 11B37
- 11B50

- Open Access

Weak Universality Theorem on the Approximation of Analytic Functions by Shifts of the Riemann Zeta-Function from a Beatty Sequence

Page range: 131 - 146

#### Abstract

In this paper, we prove a discrete analogue of Voronin’s early finite-dimensional approximation result with respect to terms from a given Beatty sequence and make use of Taylor approximation in order to derive a weak universality statement.

#### Keywords

- Universality
- Riemann zeta-function
- Beatty sequences

#### MSC 2010

- 11M99
- 30K10