Convex and Discrete Geometry is an area of mathematics situated between analysis,
geometry and discrete mathematics with numerous relations to other areas. The book gives …

Let $ A\subset {\operatorname {SL}} _n ({\mathbb R}) $ be the diagonal subgroup, and
identify ${\operatorname {SL}} _n ({\mathbb R})/{\operatorname {SL}} _n ({\mathbb Z}) $ with …

Introduction. Euclidean lattices defined over algebraic number fields have been studied in
several papers, and from different points of view. On one hand, it is often possible to …

We investigate a connection between two important classes of Euclidean lattices: well-
rounded and ideal lattices. A lattice of full rank in a Euclidean space is called well-rounded if …

The aim of this paper is to investigate rotated versions of the densest known lattices in
dimensions 2, 3, 4, 5, 6, 7, 8, 12 and 24 constructed via ideals and free Z-modules that are …

Upper bounds for Euclidean minima of algebraic number fields Page 1 Journal of Number
Theory 121 (2006) 305–323 www.elsevier.com/locate/jnt Upper bounds for Euclidean minima of …

We consider Voronoi's reduction theory of positive definite quadratic forms, which is based
on Delone subdivision. We extend it to forms and Delone subdivisions having a prescribed …

Based on algebraic number theory we construct some families of rotated Dn-lattices with full
diversity which can be good for signal transmission over both Gaussian and Rayleigh fading …

We show that the n× n Hankel matrix formed from the successive even central binomial
coefficients ( 2l l), l= 0, 1,... arises naturally when considering the trace form in the number …

In this paper we construct families of rotated D n-lattices, which may be suitable for signal
transmission over both Gaussian and Rayleigh fading channels via subfields of cyclotomic …