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Statements
θ
(
z
1
,
z
2
|
[
i
-
1
2
-
1
2
i
]
)
=
∑
n
1
=
-
∞
∞
∑
n
2
=
-
∞
∞
e
-
π
(
n
1
2
+
n
2
2
)
e
-
i
π
n
1
n
2
e
2
π
i
(
n
1
z
1
+
n
2
z
2
)
.
Riemann-theta
subscript
𝑧
1
subscript
𝑧
2
𝑖
1
2
1
2
𝑖
superscript
subscript
subscript
𝑛
1
superscript
subscript
subscript
𝑛
2
superscript
𝑒
𝜋
superscript
subscript
𝑛
1
2
superscript
subscript
𝑛
2
2
superscript
𝑒
𝑖
𝜋
subscript
𝑛
1
subscript
𝑛
2
superscript
𝑒
2
𝜋
𝑖
subscript
𝑛
1
subscript
𝑧
1
subscript
𝑛
2
subscript
𝑧
2
{\displaystyle{\displaystyle\theta\left(z_{1},z_{2}\middle|\begin{bmatrix}i&-%
\tfrac{1}{2}\\
-\tfrac{1}{2}&i\end{bmatrix}\right)=\sum_{n_{1}=-\infty}^{\infty}\sum_{n_{2}=-%
\infty}^{\infty}e^{-\pi(n_{1}^{2}+n_{2}^{2})}e^{-i\pi n_{1}n_{2}}e^{2\pi i(n_{%
1}z_{1}+n_{2}z_{2})}.}}
θ
(
𝐳
|
𝛀
)
Riemann-theta
𝐳
𝛀
{\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{%
\boldsymbol{{\Omega}}}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
Identifiers
