Hurwitz zeta function

Summary

The Hurwitz zeta function $\zeta(s, a)$ is the sum of $(n + a)^{-s}$ over all integers $n \ge 0$. It is a shifted version of the Riemann zeta function, which is the case $a = 1$. Every Dirichlet L-function modulo $q$ is $q^{-s}$ times a finite linear combination of the functions $\zeta(s, r/q)$, so their analytic properties follow from those of $\zeta(s, a)$.