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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A Mordell inequality for lattices over maximal orders


Author: Stephanie Vance
Journal: Trans. Amer. Math. Soc. 362 (2010), 3827-3839
MSC (2000): Primary 11H06, 11H31
Published electronically: February 24, 2010
MathSciNet review: 2601611
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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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Additional Information

Stephanie Vance
Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195
Address at time of publication: Department of Chemistry, Computer Science, and Mathematics, Adams State College, 208 Edgemont Boulevard, Alamosa, Colorado 81102
Email: slvance@math.washington.edu, slvance@adams.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-10-04989-5
PII: S 0002-9947(10)04989-5
Received by editor(s): October 14, 2008
Published electronically: February 24, 2010
Additional Notes: The author was supported by an ARCS Foundation fellowship and a research assistantship funded by Microsoft Research
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.