×

Dyson’s rank, overpartitions, and weak Maass forms. (English) Zbl 1130.11057

The rank of a partition (a term due to F. Dyson) is the largest part less the number of parts. An overpartition is a partition such that at most one part of each size may be overlined. Let \(\overline N(r,t, n)\) denote the number of overpartitions of \(n\) whose rank is congruent to \((\operatorname{mod} t)\). Using the theory of modular forms, especially weak Maass forms, the authors obtain interesting congruence properties of \(\overline N(r,t, n)\). These results are reminiscent of congruence properties of the partition function obtained earlier by Ono.

MSC:

11P83 Partitions; congruences and congruential restrictions
11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
PDFBibTeX XMLCite
Full Text: DOI arXiv

Online Encyclopedia of Integer Sequences:

Coefficients of the mock theta function gammabar(q).