SiegelTheta3

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

The Siegel theta function Θ[({{u}, {v}})](Ω,s) with characteristic (({{u}, {v}}))/;u=={(Subscript[u, 1]),…,(Subscript[u, r])}∧v=={(Subscript[v, 1]),…,(Subscript[v, r])}, symmetric Riemann modular matrix Ω=={{(Subscript[m, 1,1]),…,(Subscript[m, 1,r])},…,{(Subscript[m, r,1]),…,(Subscript[m, r,r])}}  with positive definite imaginary part and vector s=={(Subscript[s, 1]),…,(Subscript[s, r])}  is defined through (∑_((Subscript[n, 1])=-∞)^∞)… (∑_((Subscript[n, r])=-∞)^∞)(e^(i π ((n+u)·(Ω^T)·(n+u)+2 (n+u)·(s+v)))), where (Ω^T) means transposed to Ω matrix (or vector) and n ranges over all possible vectors in the r-dimensional integer lattice.

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