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

#### Search

- Open Access

The Sixth International Conference on Uniform Distribution Theory (UDT 2018)

Page range: i - x

#### Abstract

This volume contains papers originally presented or inspired by the Sixth International Conference on Uniform Distribution Theory, which was held at CIRM in Luminy, Marseilles, France, October 1–5, 2016.

- Open Access

Higher Order Oscillation and Uniform Distribution

Page range: 1 - 10

#### Abstract

It is known that the Möbius function in number theory is higher order oscillating. In this paper we show that there is another kind of higher order oscillating sequences in the form (^{2πiαβn g(β}_{)})_{n∈}, for a non-decreasing twice differentiable function ^{n}_{n∈} are uniformly distributed modulo 1.

#### Keywords

- higher order oscillating sequence
- uniformly distributed modulo 1 (u. d. mod 1)

#### MSC 2010

- Primary 11K65, 37A35
- Secondary 37A25, 11N05

- Open Access

Partitioning the Set of Primes to Create r -Dimensional Sequences Which are Uniformly Distributed Modulo [0, 1)^{r}

^{r}

Page range: 11 - 18

#### Abstract

Expanding on our previous results, we show that by partitioning the set of primes into a finite number of subsets of roughly the same size, we can create ^{r}

#### Keywords

- Uniform distribution modulo one

#### MSC 2010

- 11K16
- 11J71

- Open Access

Distribuion of Leading Digits of Numbers II

Page range: 19 - 42

#### Abstract

In this paper, we study the sequence (_{n}))_{n≥1},where _{n} is the _{b} x^{r}_{b}^{r}_{i}_{i}_{≥1} of the natural numbers. Especially for _{b} x^{r}

#### Keywords

- prime numbers
- Benford’s law
- distribution function
- discrepancy
- regularly varying function

#### MSC 2010

- 11K06
- 11K31
- 11K38

- Open Access

A Complete Classification of Digital (0,m, 3)-Nets and Digital (0, 2)-Sequences in Base 2

Page range: 43 - 52

#### Abstract

We give a complete classification of all matrices _{1},_{2},_{3} ∈ _{1},_{2} ∈

#### Keywords

- digital nets
- digital sequences
- classification of generating matrices

#### MSC 2010

- 11K16
- 11K38

- Open Access

On the Intriguing Search for Good Permutations

Page range: 53 - 86

#### Abstract

The intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri’s 80th birthday we aim to survey (some of) his contributions over the last four decades which considerably improved our understanding of one-dimensional van der Corput sequences and inspired a lot of related work. We recall and compare the different approaches in the search for generalised van der Corput sequences with low discrepancy, i.e., using a single generating permutation versus using a sequence of permutations. Throughout, we collect, sharpen and extend open questions which all stem from the extensive work of Henri and his coworkers and which will hopefully inspire more work in the future.

#### Keywords

- Van der Corput sequence
- low discrepancy
- permutation polynomial
- Henri Faure

#### MSC 2010

- 11K38
- 11K06
- 11T06
- 05A05

- Open Access

Notes on the Distribution of Roots Modulo a Prime of a Polynomial II

Page range: 87 - 104

#### Abstract

Let _{1} ≤ ··· ≤ _{n}_{i}_{i}_{i}

#### Keywords

- distribution
- polynomial
- roots modulo a prime

#### MSC 2010

- 11K

- Open Access

The Distributional Asymptotics Mod 1 of (log_{b} n )

_{b}n

Page range: 105 - 122

#### Abstract

This paper studies the distributional asymptotics of the slowly changing sequence of logarithms (log_{b} n_{b}

#### Keywords

- Uniformly distributed modulo one sequence
- slowly changing sequence
- rate of convergence
- Kantorovich metric
- discrepancy
- probability measures

#### MSC 2010

- 11K06
- 11K31
- 60B10
- 60E20

- Open Access

Cyclotomic Expressions for Representation Functions

Page range: 123 - 140

#### Abstract

Given a subset

#### Keywords

- Representation function
- exponential sums
- cyclotomic fields

#### MSC 2010

- 11B34
- 11B75
- 11L03
- 11R18