Define , which includes Ramanujan’s theta function as a special case. We establish a dissection identity for this function, and use it to derive congruence properties for the coefficients of . As an application we deduce several infinite families of congruences for -regular partitions and -regular bipartitions. In addition, we give a new proof of Ramanujan’s congruence for the unrestricted partition function modulo .
"Congruences for $\ell$-regular partitions and bipartitions." Rocky Mountain J. Math. 50 (2) 513 - 526, April 2020. https://doi.org/10.1216/rmj.2020.50.513