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Riemann zeta function

In mathematics, the Riemann zeta function, or Euler–Riemann zeta function, denoted by the lowercase Greek letter ⁠ ζ {\displaystyle \zeta } ⁠ (zeta), is a 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 e ( s ) > 1 {\displaystyle \mathrm {Re} (s)>1} , and its analytic continuation elsewhere.

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