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Statements
ΞΈ
β‘
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[
[
π
β’
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T
β’
π³
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[
π
β’
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β’
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π
β’
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-
1
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=
ΞΎ
β’
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πͺ
)
β’
det
β‘
[
π
β’
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+
π
]
β’
e
Ο
β’
i
β’
π³
β
[
[
π
β’
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π
]
-
1
β’
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β
π³
β’
ΞΈ
β‘
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π³
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π
)
.
Riemann-theta
delimited-[]
superscript
delimited-[]
π
π
π
1
π³
delimited-[]
π
π
π
superscript
delimited-[]
π
π
π
1
π
πͺ
delimited-[]
π
π
π
superscript
π
β
π
π
π³
delimited-[]
superscript
delimited-[]
π
π
π
1
π
π³
Riemann-theta
π³
π
{\displaystyle{\displaystyle\theta\left(\left[[\mathbf{C}\boldsymbol{{\Omega}}%
+\mathbf{D}]^{-1}\right]^{\mathrm{T}}\mathbf{z}\middle|[\mathbf{A}\boldsymbol{%
{\Omega}}+\mathbf{B}][\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]^{-1}\right)=%
\xi(\boldsymbol{{\Gamma}})\sqrt{\det[\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D%
}]}e^{\pi i\mathbf{z}\cdot\left[[\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]^{%
-1}\mathbf{C}\right]\cdot\mathbf{z}}\theta\left(\mathbf{z}\middle|\boldsymbol{%
{\Omega}}\right).}}
ΞΈ
β‘
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π³
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π
)
Riemann-theta
π³
π
{\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{%
\boldsymbol{{\Omega}}}\right)}}
Ο
{\displaystyle{\displaystyle\pi}}
det
{\displaystyle{\displaystyle\det}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
π
π
{\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
πͺ
πͺ
{\displaystyle{\displaystyle\boldsymbol{{\Gamma}}}}
ΞΎ
β’
(
πͺ
)
π
πͺ
{\displaystyle{\displaystyle\xi(\boldsymbol{{\Gamma}})}}
Identifiers
