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Moscow Mathematical Journal, 2017, Volume 17, Number 2, Pages 239–268
DOI: https://doi.org/10.17323/1609-4514-2017-17-2-239-268 (Mi mmj636) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On distances in lattices from algebraic number fields

Artūras Dubickasa, Min Shab, Igor E. Shparlinskib

a Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
b School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
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DOI: https://doi.org/10.17323/1609-4514-2017-17-2-239-268
Abstract: In this paper, we study a classical construction of lattices from number fields and obtain a series of new results about their minimum distance and other characteristics by introducing a new measure of algebraic numbers. In particular, we show that when the number fields have few complex embeddings, the minimum distances of these lattices can be computed exactly.
Key words and phrases: lattice, minimum distance, algebraic number field, Pisot numbers, multinacci number, algebraic unit.
Funding agency Grant number
Australian Research Council DP130100237
The research of the second and third named authors was supported by the Australian Research Council Grant DP130100237.
Received: January 7, 2016; in revised form November 30, 2016
Bibliographic databases:
Document Type: Article
MSC: 11H06, 11R04, 11R06, 11R09
Language: English
Citation: Artūras Dubickas, Min Sha, Igor E. Shparlinski, “On distances in lattices from algebraic number fields”, Mosc. Math. J., 17:2 (2017), 239–268
Citation in format AMSBIB
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\by Art{\=u}ras~Dubickas, Min~Sha, Igor~E.~Shparlinski
\paper On distances in lattices from algebraic number fields
\jour Mosc. Math.~J.
\yr 2017
\vol 17
\issue 2
\pages 239--268
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\crossref{https://doi.org/10.17323/1609-4514-2017-17-2-239-268}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3669873}
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    • This publication is cited in the following 3 articles:
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