DYSON'S RANK, OVERPARTITIONS, AND WEAK MAASS FORMS

By Kathrin Bringmann, Jeremy Lovejoy. 2007

60 citations recorded by the source corpus.

In a series of papers the first author and Ono connected the rank, a partition statistic intro- duced by Dyson, to weak Maass forms, a new class of functions 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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/9220facc8da2e4d681e9e26e0cf106754c25a372

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

RANK DIFFERENCES FOR OVERPARTITIONS (2007, methodology): “This is a straightforward application of Lemma 3.1.”
Partition Statistics and Quasiharmonic Maass Forms (2009, background): “Introduction and Statement of results Modular and automorphic forms play an important role in many different areas, including mathematical physics, representation theory, the theory of elliptic curves, quadratic forms, and partitions, just to mention a few.”
RANK AND CONGRUENCES FOR OVERPARTITION PAIRS (2008, background): “Instead of asking if the rank implies congruences in the sense of Theorem 1.2, we may ask if congruences for pp(n) are implied by the fact that the counting functions NN(r, t, An + B) themselves satisfy congruences.”