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On Distribution Of Well-Rounded Sublattices Of Z², Lenny Fukshansky
On Distribution Of Well-Rounded Sublattices Of Z², Lenny Fukshansky
CMC Faculty Publications and Research
A lattice is called well-rounded if its minimal vectors span the corresponding Euclidean space. In this paper we completely describe well-rounded full-rank sublattices of Z², as well as their determinant and minima sets. We show that the determinant set has positive density, deriving an explicit lower bound for it, while the minima set has density 0. We also produce formulas for the number of such lattices with a fixed determinant and with a fixed minimum. These formulas are related to the number of divisors of an integer in short intervals and to the number of its representations as a sum …
On Distribution Of Well-Rounded Sublattices Of Z², Lenny Fukshansky
On Distribution Of Well-Rounded Sublattices Of Z², Lenny Fukshansky
CMC Faculty Publications and Research
Lecture given at Institut de Mathématiques in Bordeaux, France, June 2008.