A Mordell inequality for lattices over maximal orders

Vance, Stephanie

doi:10.1090/S0002-9947-10-04989-5

A Mordell inequality for lattices over maximal orders
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by Stephanie Vance

Trans. Amer. Math. Soc. 362 (2010), 3827-3839

DOI: https://doi.org/10.1090/S0002-9947-10-04989-5

Published electronically: February 24, 2010

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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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