In mathematics, a Siegel theta series is a

Siegel modular form In mathematics, Siegel modular forms are a major type of automorphic form. These generalize conventional ''elliptic'' modular forms which are closely related to elliptic curves. The complex manifolds constructed in the theory of Siegel modular form ...

associated to a positive definite lattice, generalizing the 1-variable theta function of a lattice.

Definition

Suppose that ''L'' is a positive definite lattice. The Siegel theta series of degree ''g'' is defined by :

\Theta_L^g(T) = \sum_\exp(\pi i Tr(\lambda T \lambda^t))

where ''T'' is an element of the Siegel upper half plane of degree ''g''. This is a Siegel modular form of degree ''d'' and weight dim(''L'')/2 for some

subgroup In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G. Formally, given a group (mathematics), group under a binary operation ...

of the Siegel modular group. If the lattice ''L'' is even and unimodular then this is a Siegel modular form for the full Siegel modular group. When the degree is 1 this is just the usual theta function of a lattice.

References

*{{citation, mr=0871067 , last=Freitag, first= E. , title=Siegelsche Modulfunktionen , series=Grundlehren der Mathematischen Wissenschaften , volume= 254. Springer-Verlag, place= Berlin, year= 1983, isbn= 3-540-11661-3 Automorphic forms