  We investigate the location of zeros and poles of a dynamical zeta function
arizing in a class of lattice spin models introduced in the 60-ties by M. Kac.
The transfer operator method allows us to prove the xistence of infinitely
nontrivial zeros of this function on the real line. For certain parameter
values there exist also infinitely many trivial equally spaced zeros on a line
parallel to the imaginary axis. Hence also for this kind of dynamical zeta
function some kind of Riemann hypothesis seems to hold.
