#### Title

On the Distribution of Integral Well-rounded Lattices in Dimension Two, Part II

#### Document Type

Lecture

#### Department

Mathematics (CMC)

#### Publication Date

2-21-2007

#### Abstract

A lattice is called well-rounded if its minimal vectors span the corresponding Eucildean space. We continue studying the distribution of well-rounded full-rank sublattices of Z^2 by examining the growth of the number of such lattices with fixed determinant. We also introduce a zeta-function associated with this class of lattices and study some of its properties. By comparing its behaviour to that of two well-known zeta functions we obtain some additional information. This is continuation of the talk I gave on September 27, 2006, however I will review all the previously discussed results and background to make this talk entirely self-contained.

#### Rights Information

© 2007 Lenny Fukshansky

#### Terms of Use & License Information

#### Recommended Citation

Fukshansky, Lenny. "On the Distribution of Integral Well-rounded Lattices in Dimension Two, Part II." Number Theory Seminar, Texas A&M University, College Station, Texas. 21 February 2007.

## Comments

This lecture was given during the Number Theory Seminar at Texas A&M University in February 2007. It is a continuation of a talk by the same author: "On the distribution of integral well-rounded lattices in dimension two, Part I" given during the Number Theory Seminar at Texas A&M University in September 2006.