The theta series of a lattice is the generating function for the number of vectors with norm in the lattice.
The following table summarized lattice with closed-form theta series. Here, is a Jacobi theta function.
|lattice||theta series generating function|
|body-centered cubic lattice|
|face-centered cubic lattice|
|hexagonal close packing lattice|
|simple cubic lattice|
|tetrahedral packing lattice|
The following tables gives the first few terms of the series for these lattices.