See Power laws

The normalization C , assuming $k$ starts at $1$, is related to the Riemann zeta function, $C=\frac{1}{\zeta(\alpha)}$, or the generalized or incomplete zeta function $C=\frac{1}{\zeta(\alpha, k_{min})}$ if there is a minimum $k$ over which we normalize. Or we could approximate the sum needed to normalize by an integral. $C=\frac{1}{\int_{k_{\text{min}}}^\infty k^{-\alpha}dk}=(\alpha-1)k_{\text{min}}^{\alpha-1}$