On well-rounded ideal lattices - II

TL;DR

This paper characterizes ideal well-rounded lattices from quadratic number fields, showing that a positive proportion of such fields contain ideals that produce well-rounded lattices, extending previous work in the area.

Contribution

It provides a complete characterization of ideal well-rounded lattices in the plane and demonstrates their abundance across quadratic number fields.

Findings

A characterization of ideal well-rounded lattices in quadratic fields

A positive proportion of quadratic fields contain ideals forming well-rounded lattices

Extension of previous results on well-rounded lattices from the first author and Petersen

Abstract

We study well-rounded lattices which come from ideals in quadratic number fields, generalizing some recent results of the first author with K. Petersen. In particular, we give a characterization of ideal well-rounded lattices in the plane and show that a positive proportion of real and imaginary quadratic number fields contains ideals giving rise to well-rounded lattices.