Parity of the coefficients of certain eta-quotients, III: two special classes
Abstract
We continue a series of papers studying the parity of families of eta-quotients, which provide implications for the parity of the partition function as well as an overarching conjecture on related q-series. The present article focuses on two classes. One consists of eta-quotients of the form ft3/f1, a distinguished case of Andrews' singular overpartitions that has recently attracted attention among researchers. In addition, we investigate the parity of certain pure eta-powers f1t, appending new results to known density theorems.
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