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arXiv · 2307.03418

Rank deviations for overpartitions

Jeremy Lovejoy·Robert Osburn
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Abstract

We prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell--Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the numerous overpartition rank difference identities in the literature. We give two illustrations.

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Jeremy Lovejoy, Robert Osburn. 2023-07-07. Rank deviations for overpartitions. https://doi.org/10.1007/s40993-024-00550-5

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