  I consider the Lerch-Hurwitz or periodic zeta function as covariance function
of a periodic continuous-time stationary stochastic process. The function can
be parametrized with a continuous index $\nu$ which regulates the continuity
and differentiability properties of the process in a way completely analogous
to the parameter $\nu$ of the Mat\'ern class of covariance functions. This
makes the periodic zeta a good companion to add a power-law prior spectrum
seasonal component to a Mat\'ern prior for Gaussian process regression. It is
also a close relative of the circular Mat\'ern covariance, and likewise can be
used on spheres up to dimension three. Since this special function is not
generally available in standard libraries, I explain in detail the numerical
implementation.
