DLMF:27.10.E12 (Q8069)

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DLMF:27.10.E12
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    Statements

    Defining formula
    χ ⁡ ( n ) = G ⁡ ( 1 , χ ) k ⁢ ∑ m = 1 k χ ¯ ⁢ ( m ) ⁢ e - 2 ⁢ π ⁢ i ⁢ m ⁢ n / k . Dirichlet-character 𝑛 𝑘 Gauss-sum 1 Dirichlet-character 𝑘 superscript subscript 𝑚 1 𝑘 Dirichlet-character 𝑚 superscript 𝑒 2 imaginary-unit 𝑚 𝑛 𝑘 {\displaystyle{\displaystyle\chi\left(n\right)=\frac{G\left(1,\chi\right)}{k}% \sum_{m=1}^{k}\overline{\chi}(m)e^{-2\pi\mathrm{i}mn/k}.}}
    0 references
    DLMF id
    DLMF:27.10.E12
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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.m1addec
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