On well-rounded ideal lattices

Details On well-rounded ideal lattices On well-rounded ideal lattices

2011-01-24

arxiv.org/abs/1101.4442v3

International Journal of Number Theory, vol. 8 no. 1 (2012) pg. 189--206

Mathematics

Number Theory

15 pages; revised and corrected final version: to appear in the International Journal of Number Theory

Scientific paper

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.

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