Weyl series and the trace formula: A prescription for adding them

Periodic orbit expressions for the density of states lead to spurious resul ts when directly used to calculate quantities of thermodynamic interest. Th is is because the trace formula is usually valid only for large energies, w hile the calculations make use of it at all energies. We present a prescrip tion for circumventing this problem by isolating contributions that arise f rom the inaccurate low-energy behavior, and that are spurious, from other s ubdominant contributions that are physical and are not contained in the Wey l series. The method is tested by analyzing the fermionic grand partition f unction for a disk billiard, and may readily be extended to other dynamical systems. [S1050-2947(99)50102-9].