  We study the pattern of zeros emerging from exact partition function
evaluations of Ising spin glasses on conventional finite lattices of varying
sizes. A large number of random bond configurations are probed in the framework
of quenched averages. This study is motivated by the relationship between
hierarchical lattice models whose partition function zeros fall on Julia sets
and chaotic renormalization flows in such models with frustration, and by the
possible connection of the latter with spin glass behaviour. In any finite
volume, the simultaneous distribution of the zeros of all partition functions
can be viewed as part of the more general problem of finding the location of
all the zeros of a certain class of random polynomials with positive integer
coefficients. Some aspects of this problem have been studied in various
branches of mathematics, and we show how polynomial mappings which are used in
graph theory to classify graphs, may help in characterizing the distribution of
zeros. We finally discuss the possible limiting set as the volume is sent to
infinity.
