A Mordell Inequality for Lattices over Maximal Orders
Metric Geometry
2010-08-02 v5 Information Theory
math.IT
Number Theory
Abstract
In this paper we prove an analogue of Mordell's inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra. This inequality implies that the 16-dimensional Barnes-Wall lattice has optimal density among all 16-dimensional lattices with Hurwitz structures.
Keywords
Cite
@article{arxiv.0810.2336,
title = {A Mordell Inequality for Lattices over Maximal Orders},
author = {Stephanie Vance},
journal= {arXiv preprint arXiv:0810.2336},
year = {2010}
}
Comments
13 pages