= sum_n=1^infinity (1)/(n^s)

The image displays the definition of the Riemann zeta function.

The Riemann zeta function, denoted by $\zeta(s)$, is a function of a complex variable $s$ that plays a pivotal role in analytic number theory. It is defined by the infinite series:

$$\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}$$

This series converges for complex numbers $s$ with real part $\text{Re}(s) > 1$. The function can be extended to a meromorphic function on the entire complex plane via analytic continuation, with a simple pole at $s=1$.