DLMF:27.10.E10 (Q8067)

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DLMF:27.10.E10
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    Statements

    Defining formula
    G ⁡ ( n , χ ) = χ ¯ ⁢ ( n ) ⁢ G ⁡ ( 1 , χ ) . Gauss-sum 𝑛 Dirichlet-character Dirichlet-character 𝑛 Gauss-sum 1 Dirichlet-character {\displaystyle{\displaystyle G\left(n,\chi\right)=\overline{\chi}(n)G\left(1,% \chi\right).}}
    0 references
    DLMF id
    DLMF:27.10.E10
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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.m1abdec
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    Gauss sum
    Defining formula
    G ⁡ ( n , χ ) Gauss-sum 𝑛 Dirichlet-character {\displaystyle{\displaystyle G\left(\NVar{n},\NVar{\chi}\right)}}
    xml-id
    C27.S10.E9.m2aadec
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    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1hdec
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    Q12259
    Defining formula
    χ Dirichlet-character {\displaystyle{\displaystyle\chi}}
    xml-id
    C27.S10.XMD5.m1bdec
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