CONGRUENCES FOR l-REGULAR PARTITIONS AND BIPARTITIONS

摘要

Define F(q) := Sigma(infinity)(n=-infinity) (-1)(delta n) (an + b)q((cn2+dn)/2), 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 F (q). As an application we deduce several infinite families of congruences for l-regular partitions and l-regular bipartitions. In addition, we give a new proof of Ramanujan's congruence for the unrestricted partition function modulo 5.