  We calculate the partition function of a harmonic oscillator with
quasi-periodic boundary conditions using the zeta-function method. This work
generalizes a previous one by Gibbons and contains the usual bosonic and
fermionic oscillators as particular cases. We give an alternative prescription
for the analytic extension of the generalized Epstein function involved in the
calculation of the generalized thermal zeta-functions. We also conjecture about
the relation of our calculation to anyonic systems.
