DLMF:25.15.E4 (Q7749)

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DLMF:25.15.E4
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    Statements

    Defining formula
    L ⁡ ( s , χ ) = L ⁡ ( s , χ 0 ) ⁢ ∏ p | k ( 1 - χ 0 ⁢ ( p ) p s ) , Dirichlet-L 𝑠 𝜒 Dirichlet-L 𝑠 subscript 𝜒 0 subscript product divides 𝑝 𝑘 1 subscript 𝜒 0 𝑝 superscript 𝑝 𝑠 {\displaystyle{\displaystyle L\left(s,\chi\right)=L\left(s,\chi_{0}\right)% \prod_{p\mathbin{|}k}\left(1-\frac{\chi_{0}(p)}{p^{s}}\right),}}
    0 references
    DLMF id
    DLMF:25.15.E4
    0 references
    Symbols used
    Dirichlet $$L$$ -function
    Defining formula
    L ⁡ ( s , χ ) Dirichlet-L 𝑠 𝜒 {\displaystyle{\displaystyle L\left(\NVar{s},\NVar{\chi}\right)}}
    xml-id
    C25.S15.E1.m2acdec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1adec
    0 references
    Q12153
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C25.S1.XMD4.m1adec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1cdec
    0 references
    Q12168
    Defining formula
    χ ⁢ ( n ) 𝜒 𝑛 {\displaystyle{\displaystyle\chi(n)}}
    xml-id
    C25.S15.XMD1.m1cdec
    0 references
     
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