On Well-Rounded Ideal Lattices

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow
Kathleen Petersen, Florida State University

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.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

DOI: 10.1142/S179304211250011X

Recommended Citation

Fukshansky, Lenny, and Kathleen Petersen. "On Well-Rounded Ideal Lattices." International Journal of Number Theory 8.1 (2012): 189-206. Web.