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Well-Rounded Sublattices and Coincidence Site Lattices

  • P. ZeinerEmail author

Abstract

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.

Keywords

Zeta Function Minimal Length Planar Lattice Lattice Vector Hexagonal Lattice 
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Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Faculty of MathematicsBielefeld UniversityBielefeldGermany

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