  The $Q$-state Potts model on the simple-cubic lattice is studied using the
zeros of the exact partition function on a finite lattice. The critical
behavior of the model in the ferromagnetic and antiferromagnetic phases is
discussed based on the distribution of the zeros in the complex temperature
plane. The characteristic exponents at complex-temperature singularities, which
coexist with the physical critical points in the complex temperature plane for
no magnetic field ($H_q=0$), are estimated using the low-temperature series
expansion. We also study the partition function zeros of the Potts model for
nonzero magnetic field. For $H_q>0$ the physical critical points disappear and
the Fisher edge singularities appear in the complex temperature plane. The
characteristic exponents at the Fisher edge singularities are calculated using
the high-field, low-temperature series expansion. It seems that the Fisher edge
singularity is related to the Yang-Lee edge singularity which appears in the
complex magnetic-field plane for $T>T_c$.
