Dyson's Rank, overpartitions, and weak Maass forms

Details Dyson's Rank, overpartitions, and weak Maass forms Dyson's Rank, overpartitions, and weak Maass forms

2007-08-05

arxiv.org/abs/0708.0692v1

Mathematics

Number Theory

24 pages IMRN, accepted for publication

Scientific paper

In a series of papers the first author and Ono connected the rank, a partition statistic introduced by Dyson, to weak Maass forms, a new class of functions which are related to modular forms. Naturally it is of wide interest to find other explicit examples of Maass forms. Here we construct a new infinite family of such forms, arising from overpartitions. As applications we obtain combinatorial decompositions of Ramanujan-type congruences for overpartitions as well as the modularity of rank differences in certain arithmetic progressions.

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