DLMF:27.10.E9 (Q8066): 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.m1gdec
Property / Symbols used
 
Property / Symbols used: Q12259 / rank
 
Normal rank
Property / Symbols used: Q12259 / qualifier
 
Defining formula:

χ Dirichlet-character {\displaystyle{\displaystyle\chi}}

\Dirichletchar[]
Property / Symbols used: Q12259 / qualifier
 
xml-id: C27.S10.XMD5.m1adec

Latest revision as of 14:24, 2 January 2020

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DLMF:27.10.E9
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    Statements

    Defining formula
    G ⁡ ( n , χ ) = ∑ m = 1 k χ ⁡ ( m ) ⁢ e 2 ⁢ π ⁢ i ⁢ m ⁢ n / k . Gauss-sum 𝑛 Dirichlet-character superscript subscript 𝑚 1 𝑘 Dirichlet-character 𝑚 𝑘 superscript 𝑒 2 imaginary-unit 𝑚 𝑛 𝑘 {\displaystyle{\displaystyle G\left(n,\chi\right)=\sum_{m=1}^{k}\chi\left(m% \right)e^{2\pi\mathrm{i}mn/k}.}}
    0 references
    DLMF id
    DLMF:27.10.E9
    0 references
    Symbols defined
    Gauss sum
    0 references
    Symbols used
    Q12252
    Defining formula
    χ ⁡ ( n ) Dirichlet-character 𝑛 𝑘 {\displaystyle{\displaystyle\chi\left(\NVar{n}\right)}}
    xml-id
    C27.S8.m1aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1hdec
    0 references
    Q12239
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C27.S1.XMD3.m1edec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1gdec
    0 references
    Q12259
    Defining formula
    χ Dirichlet-character {\displaystyle{\displaystyle\chi}}
    xml-id
    C27.S10.XMD5.m1adec
    0 references
     
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