On Distribution of Well-Rounded Lattices in the Plane

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow

Document Type

Lecture

Department

Mathematics (CMC)

Publication Date

3-2-2010

Abstract

A lattice of rank N is called well-rounded (abbreviated WR) if its minimal vectors span R^N. WR lattices are extremely important for discrete optimization problems. In this talk, I will discuss the distribution of WR lattices in R^2, specifically concentrating on WR sublattices of Z^2. Studying the structure of the set C of similarity classes of these lattices, I will show that elements of C are in bijective correspondence with certain ideals in Gaussian integers, and will construct an explicit parametrization of lattices in each such similarity class by elements in the corresponding ideal. I will then use this parameterization to investigate some basic analytic properties of zeta function of WR sublattices of Z^2.

Comments

This lecture was given during the Number Theory Seminar at UC Irvine in March 2010.

Rights Information

© 2010 Lenny Fukshansky

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Recommended Citation

Fukshansky, Lenny. "On Distribution of Well-Rounded Lattices in the Plane." Number Theory Seminar, University of California -Irvine, Irvine, California. 2 March 2010.