DLMF:21.2.E5 (Q6861)

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DLMF:21.2.E5
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    Statements

    Defining formula
    θ ⁢ [ 𝜶 𝜷 ] ⁡ ( 𝐳 | 𝛀 ) = ∑ 𝐧 ∈ ℤ g e 2 ⁢ π ⁢ i ⁢ ( 1 2 ⁢ [ 𝐧 + 𝜶 ] ⋅ 𝛀 ⋅ [ 𝐧 + 𝜶 ] + [ 𝐧 + 𝜶 ] ⋅ [ 𝐳 + 𝜷 ] ) . Riemann-theta-characterstics 𝜶 𝜷 𝐳 𝛀 subscript 𝐧 𝑔 superscript 𝑒 2 𝜋 𝑖 ⋅ 1 2 delimited-[] 𝐧 𝜶 𝛀 delimited-[] 𝐧 𝜶 ⋅ delimited-[] 𝐧 𝜶 delimited-[] 𝐳 𝜷 {\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}% }}{\boldsymbol{{\beta}}}\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)=% \sum_{\mathbf{n}\in{\mathbb{Z}^{g}}}e^{2\pi i\left(\frac{1}{2}[\mathbf{n}+% \boldsymbol{{\alpha}}]\cdot\boldsymbol{{\Omega}}\cdot[\mathbf{n}+\boldsymbol{{% \alpha}}]+[\mathbf{n}+\boldsymbol{{\alpha}}]\cdot[\mathbf{z}+\boldsymbol{{% \beta}}]\right)}.}}
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    DLMF id
    DLMF:21.2.E5
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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