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

#### Search

- Open Access

Joint Distribution in Residue Classes of the Base-q and Ostrowski Digital Sums

Page range: 1 - 26

#### Abstract

Let _{q}

let _{α}(_{1},_{2} ≥ 2 be integers with

We prove that there exists _{1},_{2},

The asymptotic relation implied by this equality was proved by Coquet, Rhin & Toffin and the equality was proved for the case

#### Keywords

- Ostrowski representation
- Sum of digits function
- Joint distribution

#### MSC 2010

- 11N64
- 11N69
- 11A63

- Open Access

Chains of Truncated Beta Distributions and Benford’s Law

Page range: 27 - 32

#### Abstract

It was proved by Jang et al. that various chains of one-parameter distributions converge to Benford’s law. We study chains of truncated distributions and propose another approach, using a recent convergence result of the Lerch transcendent function, to proving that they converge to Benford’s law for initial Beta distributions with parameters

#### Keywords

- Benford’s law
- beta distribution

#### MSC 2010

- 11K06
- 60A10

- Open Access

On the Maximum Order Complexity of the Thue-Morse and Rudin-Shapiro Sequence

Page range: 33 - 42

#### Abstract

Expansion complexity and maximum order complexity are both finer measures of pseudorandomness than the linear complexity which is the most prominent quality measure for cryptographic sequences. The expected value of the

#### Keywords

- Thue-Morse sequence
- Rudin-Shapiro sequence
- automatic sequences
- maximum order complexity
- measures of pseudorandomness

#### MSC 2010

- 11B85
- 11K45

#### Abstract

Let

#### Keywords

- Freiman’s 3 − 4 Theorem
- sumset
- Lev-Smeliansky Theorem

#### MSC 2010

- Primary 11B13
- Secondary 11B75

- Open Access

Sur Les Parties Fractionnaires Des Suites (β ^{n} )_{n}_{≥1}

^{n}

_{n}

_{≥1}

Page range: 69 - 72

#### Abstract

We show that for an arbitrary sequence of intervals _{n} with constant length c, there exist real numbers ^{n} belongs to _{n} modulo one.

#### Keywords

- Distribution modulo one
- sequence of intervals
- exponential sequence

#### MSC 2010

- Primary 11K06
- 11J71

- Open Access

On the Discrepancy of Random Walks on the Circle

Page range: 73 - 86

#### Abstract

Let _{1},_{2},... be i.i.d. absolutely continuous random variables, let _{N}_{k}_{1≤}_{k}_{≤}_{N}_{N}_{k}_{1≤}_{k}_{≤}_{N}

#### Keywords

- i.i.d. sums mod 1
- empirical distribution
- discrepancy
- weak convergence

#### MSC 2010

- 11K38
- 60G50
- 60F17

- Open Access

Stable Configurations of Repelling Points on Flat Tori

Page range: 87 - 102

#### Abstract

Flat tori are analyzed in the context of an intrinsic Fourier-analytic approach to electrostatics on Riemannian manifolds, introduced by one of the authors in 1984 and previously developed for compact hyperbolic manifolds. The approach covers a large class of repelling laws, but does not naturally include laws with singularities at the origin, for which possible accommodations are discussed in the final section of the paper.

#### Keywords

- electrostatics
- tori

#### MSC 2010

- 11N64
- 11N69
- 11A63

- Open Access

Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs)

Page range: 103 - 126

#### Abstract

In the last decades many results have been proved on pseudo-randomness of binary sequences. In this series our goal is to show that using many of these results one can also construct large families of quasi-random, pseudo-random and strongly pseudo-random graphs. Indeed, it will be proved that if the first row of the adjacency matrix of a circulant graph forms a binary sequence which possesses certain pseudorandom properties (and there are many large families of binary sequences known with these properties), then the graph is quasi-random, pseudo-random or strongly pseudo-random, respectively. In particular, here in Part I we will construct large families of quasi-random graphs along these lines. (In Parts II and III we will present and study constructions for pseudo-random and

#### Keywords

- quasi-random graph
- pseudo-random graph
- pseudorandom binary sequence. Research partially supported by Hungarian National Research Development and Innovation Fund K119528

#### MSC 2010

- 05C80