DLMF:27.8.E6 (Q8052): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12253 / rank
 
Normal rank
Property / Symbols used: Q12253 / qualifier
 
Defining formula:

χ ⁡ ( n ) Dirichlet-character 𝑛 𝑘 {\displaystyle{\displaystyle\chi\left(n\right)}}

\Dirichletchar[]@@{n}{k}
Property / Symbols used: Q12253 / qualifier
 
xml-id: C27.S8.XMD1.m1edec

Latest revision as of 14:21, 2 January 2020

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DLMF:27.8.E6
No description defined

    Statements

    Defining formula
    ∑ r = 1 ϕ ⁡ ( k ) χ r ⁡ ( m ) ⁢ χ ¯ r ⁢ ( n ) = { ϕ ⁡ ( k ) , m ≡ n ( mod k ) , 0 , otherwise . superscript subscript 𝑟 1 Euler-totient-phi 𝑘 Dirichlet-character 𝑟 𝑚 𝑘 subscript Dirichlet-character 𝑟 𝑛 cases Euler-totient-phi 𝑘 modular-equivalence 𝑚 annotated 𝑛 pmod 𝑘 0 otherwise {\displaystyle{\displaystyle\sum_{r=1}^{\phi\left(k\right)}\chi_{r}\left(m% \right)\overline{\chi}_{r}(n)=\begin{cases}\phi\left(k\right),&m\equiv n\pmod{% k},\\ 0,&\mbox{otherwise}.\end{cases}}}
    0 references
    DLMF id
    DLMF:27.8.E6
    0 references
    Symbols used
    Q12252
    Defining formula
    χ ⁡ ( n ) Dirichlet-character 𝑛 𝑘 {\displaystyle{\displaystyle\chi\left(\NVar{n}\right)}}
    xml-id
    C27.S8.m1aedec
    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.m2adec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
    0 references
    Q12121
    Defining formula
    ≡ modular-equivalence {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p2.t1.r10.m10adec
    0 references
    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1edec
    0 references
    Q12239
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C27.S1.XMD3.m1adec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1ddec
    0 references
    Q12253
    Defining formula
    χ ⁡ ( n ) Dirichlet-character 𝑛 𝑘 {\displaystyle{\displaystyle\chi\left(n\right)}}
    xml-id
    C27.S8.XMD1.m1edec
    0 references
     
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