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DLMF:21.6.E8 - MaRDI portal

DLMF:21.6.E8 (Q7590)

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DLMF:21.6.E8
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    Statements

    DLMF defining formula
    θ ⁢ [ 𝜶 𝜸 ] ⁡ ( 𝐳 1 | 𝛀 ) ⁢ θ ⁢ [ 𝜷 𝜹 ] ⁡ ( 𝐳 2 | 𝛀 ) = ∑ 𝝂 ∈ ℤ g / ( 2 ⁢ ℤ g ) θ ⁢ [ 1 2 ⁢ [ 𝜶 + 𝜷 + 𝝂 ] 𝜸 + 𝜹 ] ⁡ ( 𝐳 1 + 𝐳 2 | 2 ⁢ 𝛀 ) ⁢ θ ⁢ [ 1 2 ⁢ [ 𝜶 - 𝜷 + 𝝂 ] 𝜸 - 𝜹 ] ⁡ ( 𝐳 1 - 𝐳 2 | 2 ⁢ 𝛀 ) . Riemann-theta-characterstics 𝜶 𝜸 subscript 𝐳 1 𝛀 Riemann-theta-characterstics 𝜷 𝜹 subscript 𝐳 2 𝛀 subscript 𝝂 𝑔 2 𝑔 Riemann-theta-characterstics 1 2 delimited-[] 𝜶 𝜷 𝝂 𝜸 𝜹 subscript 𝐳 1 subscript 𝐳 2 2 𝛀 Riemann-theta-characterstics 1 2 delimited-[] 𝜶 𝜷 𝝂 𝜸 𝜹 subscript 𝐳 1 subscript 𝐳 2 2 𝛀 {\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}% }}{\boldsymbol{{\gamma}}}\left(\mathbf{z}_{1}\middle|\boldsymbol{{\Omega}}% \right)\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\beta}}}{\boldsymbol{{\delta% }}}\left(\mathbf{z}_{2}\middle|\boldsymbol{{\Omega}}\right)=\sum_{\boldsymbol{% {\nu}}\in{\mathbb{Z}^{g}}/\left(2{\mathbb{Z}^{g}}\right)}\theta\genfrac{[}{]}{% 0.0pt}{}{\frac{1}{2}[\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}+\boldsymbol{{% \nu}}]}{\boldsymbol{{\gamma}}+\boldsymbol{{\delta}}}\left(\mathbf{z}_{1}+% \mathbf{z}_{2}\middle|2\boldsymbol{{\Omega}}\right)\*\theta\genfrac{[}{]}{0.0% pt}{}{\frac{1}{2}[\boldsymbol{{\alpha}}-\boldsymbol{{\beta}}+\boldsymbol{{\nu}% }]}{\boldsymbol{{\gamma}}-\boldsymbol{{\delta}}}\left(\mathbf{z}_{1}-\mathbf{z% }_{2}\middle|2\boldsymbol{{\Omega}}\right).}}
    0 references
    Symbols used
    Riemann theta function with characteristics
    DLMF defining formula
    θ ⁢ [ 𝜶 𝜷 ] ⁡ ( | missing ) Riemann-theta-characterstics 𝜶 𝜷 missing {\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\NVar{\boldsymbol{{% \alpha}}}}{\NVar{\boldsymbol{{\beta}}}}\left(\middle|missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C21.S2.E5.m2abdec
    0 references
    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2addec
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    Q10792
    DLMF defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2addec
    0 references
    positive integer
    DLMF defining formula
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C21.S1.XMD1.m1edec
    0 references
    a Riemann matrix
    DLMF defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1ddec
    0 references
    g -dimensional vector
    DLMF defining formula
    𝜶 𝜶 {\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}
    xml-id
    C21.S1.XMD4.m1bdec
    0 references
    g -dimensional vector
    DLMF defining formula
    𝜷 𝜷 {\displaystyle{\displaystyle\boldsymbol{{\beta}}}}
    xml-id
    C21.S1.XMD5.m1bdec
    0 references
    g -dimensional vector
    DLMF defining formula
    𝜹 𝜹 {\displaystyle{\displaystyle\boldsymbol{{\delta}}}}
    xml-id
    C21.S6.XMD4.m1dec
    0 references
    g -dimensional vector
    DLMF defining formula
    𝜸 𝜸 {\displaystyle{\displaystyle\boldsymbol{{\gamma}}}}
    xml-id
    C21.S6.XMD5.m1dec
    0 references

    Identifiers

     
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