Affiliation:
1. Institut für Algebra und Geometrie, KIT, FRG-76128 Karlsruhe, Germany
Abstract
Given a lattice in the plane, we consider zeta-functions encoding the number of well-rounded sublattices of a given index. We are particularly interested in the abscissa of convergence of this function and show that the quality of convergence is related to arithmeticity questions concerning the ambient lattice. In particular, we discover that there are infinitely many similarity classes of well-rounded sublattices in a plane lattice if there is at least one. This generalizes results about the rings of Gaussian and of Eisenstein integers by Fukshansky and his coauthors.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
5 articles.
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