Fractional powers of the generating function for the partition function
Volume 187 / 2019
Acta Arithmetica 187 (2019), 59-80
MSC: Primary 05A17; Secondary 11P83.
DOI: 10.4064/aa180206-10-4
Published online: 29 November 2018
Abstract
Let $p_{k}(n)$ be the coefficient of $q^n$ in the series expansion of $(q;q)_{\infty}^{k}$. It is known that the partition function $p(n)$, which corresponds to the case when $k=-1$, satisfies congruences such as $p(5n+4)\equiv 0\pmod{5}$. In this article, we discuss congruences satisfied by $p_{k}(n)$ when $k$ is a rational number.
