Bounds for the Eventual Positivity of Difference Functions of Partitions into Prime Powers

In this paper we specialize work done by Bateman and Erdos concerning difference functions of partition functions. In particular we are concerned with partitions into fixed powers of the primes. We show that any difference function of these partitionfunctions is eventually increasing, and derive explicit bounds for when it will attain strictly positive values. From these bounds an asymptotic result is derived.