20 citations · 32 across the 9 of their papers we have counts for
10 papers
On slopes of isodual lattices
Renaud Coulangeon
The slope filtration of Euclidean lattices was introduced in works by Stuhler in the late 1970s, extended by Grayson a few years later, as a new tool for reduction theory and its a…
Slopes of Euclidean lattices, tensor product and group actions
Renaud Coulangeon, Gabriele Nebe
We study the behaviour of the minimal slope of Euclidean lattices under tensor product. A general conjecture predicts that for all Euc…
Local Energy Optimality of Periodic Sets
Renaud Coulangeon, Achill Schürmann
We study the local optimality of periodic point sets in for energy minimization in the Gaussian core model, that is, for radial pair potential functions $f_c(r)=e^{-…
Computing in arithmetic groups with Voronoi's algorithm
Oliver Braun, Renaud Coulangeon, Gabriele Nebe +1
We describe an algorithm, meant to be very general, to compute a presentation of the group of units of an order in a (semi)simple algebra over Q. Our method is based on a generalis…
Spherical Designs and Heights of Euclidean Lattices
Renaud Coulangeon, Giovanni Lazzarini
We study the connection between the theory of spherical designs and the question of extrema of the height function of lattices. More precisely, we show that a full-rank n-dimension…
Perfect Lattices over Imaginary Quadratic Number Fields
Oliver Braun, Renaud Coulangeon
We present an adaptation of Voronoi theory for imaginary quadratic number fields of class number greater than 1. This includes a characterisation of extreme Hermitian forms which i…
Maximal finite subgroups and minimal classes
Renaud Coulangeon, Gabriele Nebe
We apply Voronoi's algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple $\QQ $-algebra. Thi…
The unreasonable effectiveness of the tensor product
Renaud Coulangeon, Gabriele Nebe
Using the Hermitian tensor product description of the extremal even unimodular lattice of dimension 72 found by Nebe in 2010 we show its extremality with the methods from Coulangeo…
Energy minimization, periodic sets and spherical designs
Renaud Coulangeon, Achill Schürmann
We study energy minimization for pair potentials among periodic sets in Euclidean spaces. We derive some sufficient conditions under which a point lattice locally minimizes the ene…
Spherical designs and zeta functions of lattices
Renaud Coulangeon
We set up a connection between the theory of spherical designs and the question of minima of Epstein's zeta function. More precisely, we prove that a Euclidean lattice, all layers…