Dirichlet L-function

Let $\chi$ be a Dirichlet character with conductor $f$. A Dirichlet $L$-function is $$L(\chi,s)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$

References

How Euler discovered the zeta function