Similar sublattices of planar lattices

Details Similar sublattices of planar lattices Similar sublattices of planar lattices

2009-08-18

arxiv.org/abs/0908.2558v1

Mathematics

Metric Geometry

18 pages

Scientific paper

The 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 various zeta functions of orders in imaginary quadratic fields.

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