Ramanujan Congruences for Fractional Partition Functions

Erin Bevilacqua, Kapil Chandran, Yunseo Choi

For rational $\alpha$, the fractional partition functions $p_{\alpha }(n)$ are given by the coefficients of the generating function $(q;q{)}_{\infty }^{\alpha }$. When $\alpha =-1$, one obtains the usual partitio…