Title

On Well-Rounded Ideal Lattices

Document Type

Article

Department

Mathematics (CMC)

Publication Date

2-2012

Abstract

We investigate a connection between two important classes of Euclidean lattices: well-rounded and ideal lattices. A lattice of full rank in a Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. We consider lattices coming from full rings of integers in number fields, proving that only cyclotomic fields give rise to well-rounded lattices. We further study the well-rounded lattices coming from ideals in quadratic rings of integers, showing that there exist infinitely many real and imaginary quadratic number fields containing ideals which give rise to well-rounded lattices in the plane.

Comments

This article can also be found at http://arxiv.org/pdf/1101.4442v3.pdf

Rights Information

© 2012 World Scientific Publishing Co.

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