Fixing an integer *Q* ≥ 1, the Dirichlet L-functions for characters modulo Q are linear combinations, with constant coefficients, of the ζ(*s*,*q*) where *q* = *r*/*Q* and *r* = 1, 2, ..., *Q*. This means that the Hurwitz zeta-functions for *q* a rational number have analytic properties that are closely related to that class of L-functions.

Although Hurwitz's zeta function is thought of by mathematicians as being relevant to the "purest" of mathematical disciplines, number theory, it also occurs in applied statistics; see Zipf's law and Zipf-Mandelbrot law.