The theta series of a lattice is the generating function for the number of vectors with norm
in the lattice.

Theta series for a number of lattices are implemented in the Wolfram Language as `LatticeData`[*lattice*,
`"ThetaSeriesFunction"`].

The following table summarized lattice with closed-form theta series. Here, is a Jacobi theta function.

The following tables gives the first few terms of the series for these lattices.

## See also

Coxeter-Todd Lattice,

Eisenstein Series,

Leech
Lattice
## Explore with Wolfram|Alpha

## References

Conway, J. H. and Sloane, N. J. A. *Sphere
Packings, Lattices, and Groups, 2nd ed.* New York: Springer-Verlag, 1993.Sloane,
N. J. A. Sequences A004010/M5478,
A004013/M4473, A004015/M4821,
A004018/M3218, A005875/M4092,
A008408, and A008409
in "The On-Line Encyclopedia of Integer Sequences."## Referenced
on Wolfram|Alpha

Theta Series
## Cite this as:

Weisstein, Eric W. "Theta Series." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ThetaSeries.html

## Subject classifications