  Periodic orbit expressions for the density of states lead to spurious results
when directly used to calculate quantities of thermodynamic interest. This is
because the trace formula is usually valid only for large energies while the
calculations make use of it at all energies. We present a prescription for
circumventing this problem by isolating contributions which arise from the
inaccurate low-energy behavior, and are spurious, from other subdominant
contributions which are physical and are not contained in the Weyl series. The
method is tested by analyzing the fermionic grand partition function for a disk
billiard and may readily be extended to other dynamical systems.
