DLMF:27.10.E9 (Q8066)

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DLMF:27.10.E9
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    Statements

    Defining formula
    G ⁡ ( n , χ ) = ∑ m = 1 k χ ⁡ ( m ) ⁢ e 2 ⁢ π ⁢ i ⁢ m ⁢ n / k . Gauss-sum 𝑛 Dirichlet-character superscript subscript 𝑚 1 𝑘 Dirichlet-character 𝑚 𝑘 superscript 𝑒 2 imaginary-unit 𝑚 𝑛 𝑘 {\displaystyle{\displaystyle G\left(n,\chi\right)=\sum_{m=1}^{k}\chi\left(m% \right)e^{2\pi\mathrm{i}mn/k}.}}
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    DLMF id
    DLMF:27.10.E9
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    Symbols defined
    Gauss sum
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    Symbols used
    Q12252
    Defining formula
    χ ⁡ ( n ) Dirichlet-character 𝑛 𝑘 {\displaystyle{\displaystyle\chi\left(\NVar{n}\right)}}
    xml-id
    C27.S8.m1aadec
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    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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