Siegel modular function

The Siegel theta function is a Γ_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z = X + i Y with positive definite imaginary part. It is defined by Θ(Z, s) = sum_t e^(π i t^T Z t + 2π i t^T s), where s is a complex p-vector, t is an integer p-vector that ranges over the entire p-D lattice of integers, and A^T denotes a matrix (or vector) transpose. The Siegel theta function is implemented in the Wolfram Language as SiegelTheta[Omega, s].