Riemann zeta function – Saad Quader

Riemann zeta function is a rather simple-looking function. For any number $s$ , the zeta function $\zeta(s)$ is the sum of the reciprocals of all natural numbers raised to the $s^\mathrm{th}$ power.

$\begin{array}{ccl}\zeta(s)&=&\displaystyle\sum_{n=1}^{\infty}{\frac{1}{n^s}}\\&=&1+\frac{1}{2^s}+\frac{1}{3^s}+\frac{1}{4^s}+\frac{1}{5^s}+\frac{1}{6^s}+\cdots\end{array}$

Although the variable $s$ is a complex number, for the sake of simplicity, we will treat $s$ as real. (Real numbers are a subset of complex numbers.)

Continue reading “Euler’s Product Form of Riemann Zeta Function” →