On distances in lattices from algebraic number fields

2017/03/07 by Dubickas, Arturas, Sha, Min, Shparlinski, Igor E.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1703.02163

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.

Related

• A characterization of the distances between Pisot numbers generating the same number field
• On orders in quadratic number fields with unusual sets of distances
• On the distances between Pisot numbers generating the same number field
• Structural theorems on the distance sets over finite fields
• Counting the number of distinct distances of elements in valued field\n extensions