Riemann Zeta Function

Never heard of this until someone asked my clone about this.

$\zeta (s)=\sum _{n=1}^{\infty }\frac{1}{n^s}=\frac{1}{1^s}+\frac{1}{2^s}+\frac{1}{3^s}+\cdots$

How was I supposed to have heard about this function?

• The zeta function is crucial in the study of the Prime Number Theorem, which describes how primes are distributed among natural numbers. Specifically:

The zeta function is used in proving this theorem because of its deep connections to the behavior of primes through the Euler Product formula:

$\zeta (s)={\prod }_{p\text{prime}}\frac{1}{1-p^{-s}},\text{for }\text{Re}(s)>1.$