DLMF:27.10.E11 (Q8068)

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DLMF:27.10.E11
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    Statements

    Defining formula
    | G ⁡ ( 1 , χ ) | 2 = k . superscript Gauss-sum 1 Dirichlet-character 2 𝑘 {\displaystyle{\displaystyle|G\left(1,\chi\right)|^{2}=k.}}
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    DLMF id
    DLMF:27.10.E11
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    constraint
    χ ( mod k ) annotated Dirichlet-character pmod 𝑘 {\displaystyle{\displaystyle\chi\pmod{k}}}
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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.m1acdec
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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.m2abdec
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    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1idec
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    Q12259
    Defining formula
    χ Dirichlet-character {\displaystyle{\displaystyle\chi}}
    xml-id
    C27.S10.XMD5.m1cdec
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