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The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable defined as ζ ( s ) = ∑ n = 1 ∞ 1 n s = 1 1 s + 1 2 s + 1 3 s + ⋯ {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1^{s}}}+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+\cdots } for R…
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function zeta riemann displaystyle zeros series number numbers euler values re complex frac also real known positive critical line functions
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Riemann zeta function | is a | meromorphic function on the whole complex plane | 0.90 | text |
| 12 | instance of | Examples include popular choices | 0.80 | text |
| 19 | instance of | Examples include popular choices | 0.80 | text |
| and 53.Infinite seriesThe zeta function evaluated at equidistant positive integers appears in infinite series representations of a number of constants | instance of | Examples include popular choices | 0.80 | text |
| and 53 | instance of | Examples include popular choices | 0.80 | text |
| Riemann zeta function | has application | The | 0.60 | section |
| Riemann zeta function | has application | Zipf's | 0.60 | section |
| Riemann zeta function | has application | Zipf | 0.60 | section |
| Riemann zeta function | has application | Mandelbrot | 0.60 | section |
| Riemann zeta function | has application | Lotka's | 0.60 | section |
| Riemann zeta function | has application | Zeta | 0.60 | section |
| Riemann zeta function | has application | In | 0.60 | section |
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