On Integral Well-rounded Lattices in the Plane

On distribution of integral well-rounded lattices in the plane

Well-Rounded Zeta-Function of Planar Arithmetic Lattices

We investigate the properties of the zeta-function of well-rounded sublattices of a fixed arithmetic lattice in the plane. In particular, we show that this function has abscissa of convergence at s = 1 with a real pole of order 2, improving upon a result of [11]. We use this result to show that the number of well-rounded sublattices of a planar arithmetic lattice of index less or equal N is O(N...

ON WELL - ROUNDED IDEAL LATTICES 3 Theorem 1

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 ...

On Well-rounded Ideal Lattices

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 ...

On Well-rounded Ideal Lattices - Ii

We study well-rounded lattices which come from ideals in quadratic number fields, generalizing some recent results of the first author with K. Petersen [8]. 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.