On well-rounded ideal lattices

Lenny Fukshansky, Kathleen Petersen

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)189-206
Number of pages18
JournalInternational Journal of Number Theory
Issue number1
StatePublished - Feb 2012
Externally publishedYes


  • binary quadratic forms
  • ideal lattices
  • quadratic number fields
  • Well-rounded lattices


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