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Mock modularity of the M-d-rank of overpartitions Public Deposited

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https://ir.library.oregonstate.edu/concern/articles/w3763d051

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  • 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 holomorphic part of a certain harmonic Maass form of weight 1/2. We give the exact transformation of this harmonic Maass form along with a few identities for the M-d-rank. (C) 2018 Elsevier Inc. All rights reserved.
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  • 466
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  • 0022-247X

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