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On distribution of well-rounded sublattices of Z^2
by
Lenny Fukshansky
Claremont McKenna College
A lattice is called well-rounded if its minimal vectors span the corresponding Euclidean space. We study the distribution of well-rounded sublattices of Z^2 by means of investigating basic analytic properties of the corresponding zeta function, i.e. the determinantal Dirichlet series over all such lattices. In particular, we discuss the order of the pole, growth of coefficients, and some related features of this and some related Dirichlet series. Our key tool is a convenient parametrization of similarity classes of such lattices by certain ideals in Gaussian integers, along with a simple combinatorial structure on the set of all such similarity classes.
Date received: April 27, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-33.