DLMF:27.11.E11 (Q8080)

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DLMF:27.11.E11
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    Statements

    Defining formula
    ∑ p ≤ x p ≡ h ( mod k ) ln ⁡ p p = 1 ϕ ⁡ ( k ) ⁢ ln ⁡ x + O ⁡ ( 1 ) , subscript 𝑝 𝑥 modular-equivalence 𝑝 annotated ℎ pmod 𝑘 𝑝 𝑝 1 Euler-totient-phi 𝑘 𝑥 Big-O 1 {\displaystyle{\displaystyle\sum_{\begin{subarray}{c}p\leq x\\ p\equiv h\!\!\!\!\!\pmod{k}\end{subarray}}\frac{\ln p}{p}=\frac{1}{\phi\left(k% \right)}\ln x+O\left(1\right),}}
    0 references
    DLMF id
    DLMF:27.11.E11
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2ajdec
    0 references
    Euler’s totient
    Defining formula
    ϕ ⁡ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E7.m2acdec
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