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Statements
θ
^
(
x
1
+
i
y
1
,
x
2
+
i
y
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|
[
i
-
1
2
-
1
2
i
]
)
=
∑
n
1
=
-
∞
∞
∑
n
2
=
-
∞
∞
e
-
π
(
n
1
+
y
1
)
2
-
π
(
n
2
+
y
2
)
2
e
π
i
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2
n
1
x
1
+
2
n
2
x
2
-
n
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n
2
)
.
Riemann-theta-hat
subscript
𝑥
1
𝑖
subscript
𝑦
1
subscript
𝑥
2
𝑖
subscript
𝑦
2
𝑖
1
2
1
2
𝑖
superscript
subscript
subscript
𝑛
1
superscript
subscript
subscript
𝑛
2
superscript
𝑒
𝜋
superscript
subscript
𝑛
1
subscript
𝑦
1
2
𝜋
superscript
subscript
𝑛
2
subscript
𝑦
2
2
superscript
𝑒
𝜋
𝑖
2
subscript
𝑛
1
subscript
𝑥
1
2
subscript
𝑛
2
subscript
𝑥
2
subscript
𝑛
1
subscript
𝑛
2
{\displaystyle{\displaystyle\hat{\theta}\left(x_{1}+iy_{1},x_{2}+iy_{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}+y_{1})^{2}-\pi(n_{2}+y_{2})^{2}}\*e^{\pi i(2n_{1%
}x_{1}+2n_{2}x_{2}-n_{1}n_{2})}.}}
θ
^
(
𝐳
|
𝛀
)
Riemann-theta-hat
𝐳
𝛀
{\displaystyle{\displaystyle\hat{\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}}}
