A Mordell Inequality for Lattices over Maximal Orders

Stephanie Vance

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arXiv · 0810.2336

A Mordell Inequality for Lattices over Maximal Orders

Stephanie Vance

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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.

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BibTeX RIS

Stephanie Vance. 2010-07-30. A Mordell Inequality for Lattices over Maximal Orders. https://arxiv.org/abs/0810.2336

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