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Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter $ζ$ (zeta), is a mathematical function of a complex variable defined as ${\\displaystyle \\zeta (s)=\\sum _{n=1}^{\\infty }{\ rac {1}{n^{s}}}={\ rac {1}{1^{s}}}+{\ rac {1}{2^{s}}}+{\ rac {1}{3^{s}}}+\\cdots }$ for ${\\displaystyle \\operatorname {Re} (s)>1}$ , and its analytic continuation elsewhere.
The Riemann zeta function plays a pivotal role in analytic number theory, and has applications in physics, probability theory, and applied statistics.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riemann_zeta_function)

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