DLMF:21.2.E5 (Q6861)

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DLMF:21.2.E5
No description defined

    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)}.}}
    0 references
    DLMF id
    DLMF:21.2.E5
    0 references
    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
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q10818
    Defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2aadec
    0 references
    Q11959
    Defining formula
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C21.S1.XMD1.m1adec
    0 references
    Q11960
    Defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1bdec
    0 references
    Q11961
    Defining formula
    𝜶 𝜶 {\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}
    xml-id
    C21.S1.XMD4.m1dec
    0 references
    Q11962
    Defining formula
    𝜷 𝜷 {\displaystyle{\displaystyle\boldsymbol{{\beta}}}}
    xml-id
    C21.S1.XMD5.m1dec
    0 references
     
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