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DLMF:21.5.E5 - MaRDI portal

DLMF:21.5.E5 (Q7577)

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DLMF:21.5.E5
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    Statements

    DLMF defining formula
    𝚪 = [ 𝐀 𝟎 g 𝟎 g [ 𝐀 - 1 ] T ] ⇒ θ ⁡ ( 𝐀𝐳 | 𝐀 ⁢ 𝛀 ⁢ 𝐀 T ) = θ ⁡ ( 𝐳 | 𝛀 ) . 𝚪 𝐀 subscript 0 𝑔 subscript 0 𝑔 delimited-[] superscript 𝐀 1 ⇒ Riemann-theta 𝐀𝐳 𝐀 𝛀 𝐀 Riemann-theta 𝐳 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Gamma}}=\begin{bmatrix}\mathbf{A}&% \boldsymbol{{0}}_{g}\\ \boldsymbol{{0}}_{g}&[\mathbf{A}^{-1}]^{\mathrm{T}}\end{bmatrix}\Rightarrow% \theta\left(\mathbf{A}\mathbf{z}\middle|\mathbf{A}\boldsymbol{{\Omega}}\mathbf% {A}^{\mathrm{T}}\right)=\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}% \right).}}
    0 references
    Symbols used
    Riemann theta function
    DLMF defining formula
    θ ⁡ ( 𝐳 | 𝛀 ) Riemann-theta 𝐳 𝛀 {\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{% \boldsymbol{{\Omega}}}\right)}}
    xml-id
    C21.S2.E1.m2aadec
    0 references
    positive integer
    DLMF defining formula
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C21.S1.XMD1.m1adec
    0 references
    a Riemann matrix
    DLMF defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1adec
    0 references
    21.5.E1
    DLMF defining formula
    𝚪 𝚪 {\displaystyle{\displaystyle\boldsymbol{{\Gamma}}}}
    xml-id
    C21.S5.XMD1.m1ddec
    0 references

    Identifiers

     
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