Rank differences for overpartitions

Details Rank differences for overpartitions Rank differences for overpartitions

2007-03-12

arxiv.org/abs/math/0703326v2

The Quarterly Journal of Mathematics 59 (2008), 257-273

Mathematics

Number Theory

17 pages, final version, accepted for publication in the Quarterly Journal of Mathematics

Scientific paper

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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