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 | References | Similar Articles | Additional Information

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 -dimensional Barnes-Wall lattice has optimal density among all -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:
https://doi.org/10.1090/S0002-9947-10-04989-5

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.