SiegelTheta

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

The Siegel theta function Θ(Ω,s) with 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·(Ω^T)·n+2 n·s))), 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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