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On the Existence of Similar Sublattices

Conway, J. H. and Rains, E. M. and Sloane, N. J. A. (1999) On the Existence of Similar Sublattices. Canadian Journal of Mathematics, 51 (6). pp. 1300-1306. ISSN 0008-414X. doi:10.4153/CJM-1999-059-5.

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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?

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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.
Issue or Number:6
Classification Code:MSC: 52C07
Record Number:CaltechAUTHORS:20170926-102111766
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81832
Deposited By: Tony Diaz
Deposited On:26 Sep 2017 17:40
Last Modified:15 Nov 2021 19:46

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