Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols

By Kathrin Bringmann, Jeremy Lovejoy, Robert Osburn. 2008

53 citations recorded by the source corpus.

We define two-parameter generalizations of Andrews' (k+1)-marked odd Durfee sym- bols and 2kth symmetrized odd rank moments, and study the automorphic properties of some of their generating functions. When k = 0 we obtain families of modular forms and mock modular forms. When k � 1, we find quasimodular forms and quasimock modular forms.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7777c4d5cfd70b35e2397c9b5c2d7960e055d5c6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Chris Jennings-Shaffer
2. Frank G. Garvan
3. Kathrin Bringmann
4. Karl Mahlburg
5. Jeremy Lovejoy
6. Robert Osburn

In Discrete Mathematics and Combinatorics

1. Chris Jennings-Shaffer
2. Frank G. Garvan
3. Kathrin Bringmann
4. Karl Mahlburg

In Geometry and Topology

1. Chris Jennings-Shaffer
2. Frank G. Garvan

Citations in the corpus

• Higher Order SPT-Functions (2010, background): “Analytic and arithmetic properties of higher order rank moments were studied by Bringmann, Lovejoy and Osburn [9] and by Bringmann, the author and Mahlburg [8].”
• The spt-crank for overpartitions (2013, background): “The generating functions for the spt functions are given as follows; these are special cases of a general SPT function due to Bringmann, Lovejoy, and Osburn [15, Section 7], SPT( d, e ; q ) = ( − dq ; q ) ∞ ( − eq ; q ) ∞ ( deq ; q ) ∞ ( q ; q ) ∞ ∞ n =1 q n ( q ; q ) n ( deq ; q ) n (1 − q n ) 2 ( ”