Geodesic
Similar Sublattices of Planar Lattices
Canadian journal of mathematics, Tome 63 (2011) no. 6, pp. 1220-1237

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DOI

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 zeta functions of orders in imaginary quadratic fields.
DOI : 10.4153/CJM-2011-019-9
Mots-clés : 11H06, 11R11, 52C05, 82D25 
Baake, Michael; Scharlau, Rudolf; Zeiner, Peter. Similar Sublattices of Planar Lattices. Canadian journal of mathematics, Tome 63 (2011) no. 6, pp. 1220-1237. doi: 10.4153/CJM-2011-019-9
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     title = {Similar {Sublattices} of {Planar} {Lattices}},
     journal = {Canadian journal of mathematics},
     pages = {1220--1237},
     year = {2011},
     volume = {63},
     number = {6},
     doi = {10.4153/CJM-2011-019-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-019-9/}
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