Moscow Mathematical Journal

Volume 17, Issue 2, April–June 2017 pp. 239–268.

On Distances in Lattices from Algebraic Number Fields

Authors: Artūras Dubickas (1), Min Sha (2), and Igor E. Shparlinski (2)
Author institution:(1) Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
(2) School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

Summary:

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.

2010 Math. Subj. Class. 11H06, 11R04, 11R06, 11R09.

Keywords: Lattice, minimum distance, algebraic number field, Pisot numbers, multinacci number, algebraic unit.

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