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

#### Search

- Open Access

On the Distribution of αp Modulo One in Quadratic Number Fields

Page range: 1 - 48

#### Abstract

We investigate the distribution of

#### Keywords

- distribution modulo one
- Diophantine approximation
- sieve methods
- sums over primes
- quadratic field
- smoothed sum
- Poisson summation

#### MSC 2010

- Primary 11J17
- Secondary 11J71
- 11N35
- 11N36
- 11L20
- 11L07
- 11K60

#### Abstract

K. Mahler’s conjecture: There exists no ^{+} such that the fractional parts {^{n}} satisfy 0 ^{n}} < 1/2 for all _{n}^{n}}, _{0}(_{0}(

#### Keywords

- distribution function
- fractional part
- -number

#### MSC 2010

- Primary: 11K06
- Secondary: 11K31
- 11J71

- Open Access

Divisibility Parameters and the Degree of Kummer Extensions of Number Fields

Page range: 71 - 88

#### Abstract

Let _{1},..._{r}^{×} ^{×} _{1},..._{r}_{i}_{ℓ}^{m},
_{ℓ}^{m}_{1},..._{r}, m

#### Keywords

- number field
- Kummer theory
- Kummer extension
- degree

#### MSC 2010

- Primary:11Y40
- Secondary:11R20,11R21

- Open Access

Balance and Pattern Distribution of Sequences Derived from Pseudorandom Subsets of ℤ_{q}

_{q}

Page range: 89 - 108

#### Abstract

Let _{n}_{n} ≡ x_{n}_{+1} _{n}

(2) For an integer _{n}

(3) Let (_{n}

We study the balance and pattern distribution of the sequences (_{n}_{n}_{n}

(1) The sequence (_{n}

(2) The sequence (_{n}

(3) The sequence (_{n}^{q}_{2}.

These results are motivated by earlier results for the sets of quadratic residues and primitive roots modulo a prime. We unify these results and derive many further (asymptotically) balanced sequences with uniform pattern distribution from pseudorandom subsets.

#### Keywords

- sequence
- pseudorandom subset
- balance
- pattern distribution
- correlation measure

#### MSC 2010

- 11K45
- 94A55
- 11T71
- 11Z05

- Open Access

From Randomness in Two Symbols to Randomness in Three Symbols

Page range: 109 - 128

#### Abstract

In 1909 Borel defined normality as a notion of randomness of the digits of the representation of a real number over certain base (fractional expansion). If we think of the representation of a number over a base as an infinite sequence of symbols from a finite alphabet

#### Keywords

- Normal numbers
- combinatorics on words
- Champernowne number

#### MSC 2010

- Primary 11K16
- 05A05

- Open Access

AO. Univ.-Prof. Dr. Reinhard Winkler (1964–2021) An Obituary

Page range: 129 - 136