CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: All articles in the CMB digital archive with keyword Gaussian integers

  Expand all        Collapse all Results 1 - 3 of 3

1. CMB Online first

Jensen, Gerd; Pommerenke, Christian
On the structure of the Schild group in Relativity Theory
Alfred Schild has established conditions that Lorentz transformations map world-vectors $(ct,x,y,z)$ with integer coordinates onto vectors of the same kind. These transformations are called integral Lorentz transformations. The present paper contains supplements to our earlier work with a new focus on group theory. To relate the results to the familiar matrix group nomenclature we associate Lorentz transformations with matrices in $\mathrm{SL}(2,\mathbb{C})$. We consider the lattice of subgroups of the group originated in Schild's paper and obtain generating sets for the full group and its subgroups.

Keywords:Lorentz transformation, integer lattice, Gaussian integers, Schild group, subgroup
Categories:22E43, 20H99, 83A05

2. CMB 2015 (vol 59 pp. 123)

Jensen, Gerd; Pommerenke, Christian
Discrete Space-time and Lorentz Transformations
Alfred Schild has established conditions that Lorentz transformations map world-vectors $(ct,x,y,z)$ with integer coordinates onto vectors of the same kind. The problem was dealt with in the context of tensor and spinor calculus. Due to Schild's number-theoretic arguments, the subject is also interesting when isolated from its physical background. The paper of Schild is not easy to understand. Therefore we first present a streamlined version of his proof which is based on the use of null vectors. Then we present a purely algebraic proof that is somewhat shorter. Both proofs rely on the properties of Gaussian integers.

Keywords:Lorentz transformation, integer lattice, Gaussian integers
Categories:22E43, 20H99, 83A05

3. CMB 2011 (vol 56 pp. 161)

Rêgo, L. C.; Cintra, R. J.
An Extension of the Dirichlet Density for Sets of Gaussian Integers
Several measures for the density of sets of integers have been proposed, such as the asymptotic density, the Schnirelmann density, and the Dirichlet density. There has been some work in the literature on extending some of these concepts of density to higher dimensional sets of integers. In this work, we propose an extension of the Dirichlet density for sets of Gaussian integers and investigate some of its properties.

Keywords:Gaussian integers, Dirichlet density
Categories:11B05, 11M99, 11N99

© Canadian Mathematical Society, 2016 : https://cms.math.ca/