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A MORDELL INEQUALITY FOR LATTICES OVER MAXIMAL ORDERS

STEPHANIE VANCE
Transactions of the American Mathematical Society
Vol. 362, No. 7 (JULY 2010), pp. 3827-3839
Stable URL: http://www.jstor.org/stable/25677850
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A MORDELL INEQUALITY FOR LATTICES OVER MAXIMAL ORDERS
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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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