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Rank differences for overpartitions

Jeremy Lovejoy·Robert Osburn
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Abstract

In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulas for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulas for the generating functions for rank differences for overpartitions. These are in terms of modular functions and generalized Lambert series.

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Jeremy Lovejoy, Robert Osburn. 2007-03-12. Rank differences for overpartitions. https://doi.org/10.1093/qmath/ham031

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