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A MORDELL INEQUALITY FOR LATTICES OVER MAXIMAL ORDERS
Transactions of the American Mathematical Society
Vol. 362, No. 7 (JULY 2010), pp. 3827-3839
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/25677850
Page Count: 13
You can always find the topics here!Topics: Mathematical lattices, Mathematical vectors, Mathematical inequalities, Determinants, Spheres, Euclidean space, Mathematical problems, Integers, Quaternions, Algebra
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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.
Transactions of the American Mathematical Society © 2010 American Mathematical Society