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

#### Search

#### Abstract

- Open Access

An Improved Bound for the Star Discrepancy of Sequences in the Unit Interval

Page range: 1 - 14

#### Abstract

It is known that there is a constant _{1}, _{2}, . . . in [0, 1) we have for the star discrepancy ^{∗} be the supremum of all such ^{∗} > 0.065664679 . . . , thereby slightly improving the estimates known until now.

#### Keywords

- uniform distribution
- discrepancy

#### MSC 2010

- 11K38
- 11K06

- Open Access

Uniform Distribution of the Sequence of Balancing Numbers Modulo m

Page range: 15 - 21

#### Abstract

The balancing numbers and the balancers were introduced by Behera et al. in the year 1999, which were obtained from a simple diophantine equation. The goal of this paper is to investigate the moduli for which all the residues appear with equal frequency with a single period in the sequence of balancing numbers. Also, it is claimed that, the balancing numbers are uniformly distributed modulo 2, and this holds for all other powers of 2 as well. Further, it is shown that the balancing numbers are not uniformly distributed over odd primes.

#### Keywords

- Balancing numbers
- Balancers
- Uniform distribution
- Periodicity of balancing numbers

#### MSC 2010

- 11B37
- 11B39

- Open Access

Distribution of Leading Digits of Numbers

Page range: 23 - 45

#### Abstract

Applying the theory of distribution functions of sequences we find the relative densities of the first digits also for sequences _{n}_{n}^{r}_{n}

#### Keywords

- Benford’s law
- distribution function
- prime number

#### MSC 2010

- 11K06
- 11K31

- Open Access

On the Pseudorandomness of the Liouville Function of Polynomials over a Finite Field

Page range: 47 - 58

#### Abstract

We study several pseudorandom properties of the Liouville function and the Möbius function of polynomials over a finite field. More precisely, we obtain bounds on their balancedness as well as their well-distribution measure, correlation measure, and linear complexity profile.

#### Keywords

- polynomials
- finite fields
- irreducible factors
- pseudorandom sequence
- balancedness
- well-distribution
- correlation measure
- linear complexity
- polynomial Liouville function
- polynomial Möbius function

#### MSC 2010

- 11K45
- 11T06
- 11T24
- 11T71

#### Abstract

We introduce the concept of strong normality by defining strong normal numbers and provide various properties of these numbers, including the fact that almost all real numbers are strongly normal.

#### Keywords

- normal numbers
- uniform distribution modulo 1

#### MSC 2010

- 11K16
- 11N37

- Open Access

On the Conjecture of Lehmer, Limit Mahler Measure of Trinomials and Asymptotic Expansions

Page range: 79 - 139

#### Abstract

Let _{n}_{n}_{n}_{n}_{j,n}_{n}_{n}_{n}_{n}

#### Keywords

- Mahler measure
- trinomial
- Lehmer Conjecture
- asymptotic expansion
- divergent series
- Perron number
- Pisot number
- Schinzel-Zassenhaus conjecture
- Smyth conjecture
- Lind-Boyd Conjecture
- Boyd Conjecture
- Erdős-Turán-Mignotte-Amoroso
- discrepancy function
- limit equidistribution

#### MSC 2010

- 11C08
- 11G50
- 11K16
- 11K26
- 11K38
- 11Q05
- 11R06
- 11R09
- 30B10
- 30C15

- Open Access

On Hausdorff Dimensions Related to Sets with Given Asymptotic and Gap Densities

Page range: 141 - 157

#### Abstract

For a set _{1}_{2}_{A}

#### Keywords

- Sequences of integers
- lower asymptotic density
- upper asymptotic density
- gap density
- Hausdorff dimension

#### MSC 2010

- 11B05
- 11K55

- Open Access

Pair Correlations and Random Walks on the Integers

Page range: 159 - 164

#### Abstract

The paper gives conditions for a sequence of fractional parts of real numbers

#### Keywords

- pair correlation
- random walks

#### MSC 2010

- 11K38
- 60G50

- Open Access

On Small Sets of Distribution Functions of Ratio Block Sequences

Page range: 165 - 174

#### Abstract

There are various methods how to describe and characterize distribution of elements of sets of positive integers. One of the most interesting is that using the set of all distribution functions of the corresponding ratio block sequence introduced in [Strauch, O.—Tóth, J.T.: Publ. Math. Debrecen

#### Keywords

- asymptotic distribution function
- uniform distribution
- block sequence

#### MSC 2010

- 11B05

- Open Access

Linear Recursive Odometers and Beta-Expansions

Page range: 175 - 186

#### Abstract

The aim of this paper is to study the connection between different properties related to

#### Keywords

- beta-expansions
- odometer
- purely discrete spectrum
- finiteness property

#### MSC 2010

- 11A63
- 11K16
- 11B37
- 28D05