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DLMF:21.7.E9 - MaRDI portal

DLMF:21.7.E9 (Q7601)

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DLMF:21.7.E9
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    Statements

    DLMF defining formula
    E ⁒ ( P 1 , P 2 ) = ΞΈ ⁒ [ 𝜢 𝜷 ] ⁑ ( ∫ P 1 P 2 𝝎 | 𝛀 ) / ( ΞΆ ⁒ ( P 1 ) ⁒ ΞΆ ⁒ ( P 2 ) ) , 𝐸 subscript 𝑃 1 subscript 𝑃 2 Riemann-theta-characterstics 𝜢 𝜷 superscript subscript subscript 𝑃 1 subscript 𝑃 2 𝝎 𝛀 𝜁 subscript 𝑃 1 𝜁 subscript 𝑃 2 {\displaystyle{\displaystyle E(P_{1},P_{2})=\theta\genfrac{[}{]}{0.0pt}{}{% \boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}\left(\int_{P_{1}}^{P_{2}}% \boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)\Bigg{/}\left(\sqrt{% \zeta(P_{1})}\sqrt{\zeta(P_{2})}\right),}}
    0 references
    Symbols used
    Riemann theta function with characteristics
    DLMF defining formula
    θ ⁒ [ 𝜢 𝜷 ] ⁑ ( | missing ) Riemann-theta-characterstics 𝜢 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
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q10751
    DLMF defining formula
    ( a , b ) π‘Ž 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6adec
    0 references
    a Riemann matrix
    DLMF defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1bdec
    0 references
    g -dimensional vector
    DLMF defining formula
    𝜢 𝜢 {\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
    points
    DLMF defining formula
    P 1 , P 2 subscript 𝑃 1 subscript 𝑃 2 {\displaystyle{\displaystyle P_{1},P_{2}}}
    xml-id
    C21.S7.XMD8.m1dec
    0 references
    vector of differentials
    DLMF defining formula
    𝝎 𝝎 {\displaystyle{\displaystyle\boldsymbol{{\omega}}}}
    xml-id
    C21.S7.XMD9.m1dec
    0 references

    Identifiers

     
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