A Mordell Inequality for Lattices over Maximal Orders

Details A Mordell Inequality for Lattices over Maximal Orders A Mordell Inequality for Lattices over Maximal Orders

2008-10-14

arxiv.org/abs/0810.2336v5

Trans. Amer. Math. Soc. 362 (2010), no. 7, 3827-3839

Mathematics

Metric Geometry

13 pages

Scientific paper

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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