Published December 1999
| Submitted + Published
Journal Article
Open
On the Existence of Similar Sublattices
- Creators
- Conway, J. H.
-
Rains, E. M.
- Sloane, N. J. A.
Chicago
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Abstract
Partial answers are given to two questions. When does a lattice Λ contain a sublattice Λ′ of index that is geometrically similar to Λ? When is the sublattice "clean", in the sense that the boundaries of the Voronoi cells for Λ' do not intersect Λ?
Additional Information
© 1999 Canadian Mathematical Society. Received by the editors November 11, 1998; revised October 12, 1999. We thank H.-G. Quebbemann for suggesting that the similar sublattice problem is best handled via the Hilbert symbol, and for pointing out an error in the first version of this paper. We also thank V. A. Vaishampayan and S. D. Servetto for many conversations concerning vector quantization, and M. Baake and J.Martinet for comments on the manuscript. R. Schulze-Pillot drew our attention to the Chapman references.Attached Files
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Additional details
- Eprint ID
- 81832
- Resolver ID
- CaltechAUTHORS:20170926-102111766
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2017-09-26Created from EPrint's datestamp field
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2021-11-15Created from EPrint's last_modified field