Author:
Baake Michael,Scharlau Rudolf,Zeiner Peter
Abstract
AbstractThe similar sublattices of a planar lattice can be classified via its multiplier ring. The latter is the ring of rational integers in the generic case, and an order in an imaginary quadratic field otherwise. Several classes of examples are discussed, with special emphasis on concrete results. In particular, we derive Dirichlet series generating functions for the number of distinct similar sublattices of a given index, and relate them to zeta functions of orders in imaginary quadratic fields.
Publisher
Canadian Mathematical Society
Cited by
6 articles.
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1. Similar Sublattices and Submodules;2019-20 MATRIX Annals;2021
2. Similarity isometries of point packings;Acta Crystallographica Section A Foundations and Advances;2020-10-19
3. CLASSIFICATION OF THE SUBLATTICES OF A LATTICE;Bulletin of the Australian Mathematical Society;2020-04-13
4. Well-rounded sublattices of planar lattices;Acta Arithmetica;2014
5. Well-Rounded Sublattices and Coincidence Site Lattices;Aperiodic Crystals;2013