Well-Rounded Sublattices and Coincidence Site Lattices
A lattice is called well-rounded, if its lattice vectors of minimal length span the ambient space. We show that there are interesting connections between the existence of well-rounded sublattices and coincidence site lattices (CSLs). Furthermore, we count the number of well-rounded sublattices for several planar lattices and give their asymptotic behaviour.
KeywordsZeta Function Minimal Length Planar Lattice Lattice Vector Hexagonal Lattice
The author thanks M. Baake, and R. Scharlau, for fruitful discussions. This work was supported by the German Research Council (DFG) within the CRC 701.
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