We investigate the modular properties of a new partition rank, the M-d-rank of overpartitions. In fact this is an infinite family of ranks, indexed by the positive integer d, that gives both the Dyson rank of overpartitions and the overpartition M-2-rank as special cases. The M-d-rank of overpartitions is the...
Recently, Duke and Jenkins have studied a certain family of modular forms fk,m, that form a natural basis of the space of weakly holomorphic modular forms of weight k on SL2(Z). In particular, they prove that for all but at most [k/12] + 1 values of m, the zeros of...