Riemann zeta function

Analytic function in mathematicsThe Riemann zeta function ζ(z) plotted with domain coloringThe pole at z = 1 and two zeros on the critical lineIn mathematics, the Riemann zeta function, or Euler–Riemann zeta function, denoted by the lowercase Greek letter⁠ζ{\displaystyle \zeta }⁠ (zeta), is a function of a complex variable defined as ζ(s)=∑n=1∞1ns=11s+12s+13s+⋯{\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 Re(s)>1…