# ON THE PARITY OF THE PARTITION FUNCTION

@inproceedings{Robbins1995ONTP, title={ON THE PARITY OF THE PARTITION FUNCTION}, author={Neville Robbins}, year={1995} }

Although much is known about the partition function, little is known about its parity. For the polynomials D(x) := (Dx + 1)/24, where D ≡ 23 (mod 24), we show that there are infinitely many m (resp. n) for which p(D(m)) is even (resp. p(D(n)) is odd) if there is at least one such m (resp. n). We bound the first m and n (if any) in terms of the class number h(−D). For prime D we show that there are indeed infinitely many even values. To this end we construct new modular generating functions…

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