A New Lower Bound on the Number of Odd Values of the Ordinary Partition Function

The parity of p(n), the ordinary partition function, has been studied for at least a century, yet it still remains something of a mystery. Although much work has been done, the known lower bounds for the number of even and odd values of p(n) for n ≤ N still appear to have a great deal of room for improvement. In this paper, we use classical methods to give a new lower bound for the number of odd values of p(n).