Partition statistics and quasiweak Maass forms

Details Partition statistics and quasiweak Maass forms Partition statistics and quasiweak Maass forms

2008-03-13

arxiv.org/abs/0803.1891v2

Mathematics

Number Theory

Scientific paper

Andrews recently introduced k-marked Durfee symbols, which are a generalization of partitions that are connected to moments of Dyson's rank statistic. He used these connections to find identities relating their generating functions as well as to prove Ramanujan-type congruences for these objects and find relations between. In this paper we show that the hypergeometric generating functions for these objects are natural examples of quasimock theta functions, which are defined as the holomorphic parts of weak Maass forms and their derivatives. In particular, these generating functions may be viewed as analogs of Ramanujan's mock theta functions with arbitrarily high weight. We use the automorphic properties to prove the existence of infinitely many congruences for the Durfee symbols. Furthermore, we show that as k varies, the modularity of the k-marked Durfee symbols is precisely dictated by the case k=2. Finally, we use this relation in order to prove the existence of general congruences for rank moments in terms of level one modular forms of bounded weight.

Affiliated with

Also associated with

No associations

Rating

Partition statistics and quasiweak Maass forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Partition statistics and quasiweak Maass forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Partition statistics and quasiweak Maass forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-69521