Mock modular forms and singular combinatorial series

Amanda Folsom, and Susie Kimport. "Mock modular forms and singular combinatorial series." Acta Arithmetica 159.3 (2013): 257-297. <http://eudml.org/doc/279233>.

@article{AmandaFolsom2013,
abstract = {A celebrated result of Bringmann and Ono shows that the combinatorial rank generating function exhibits automorphic properties after being completed by the addition of a non-holomorphic integral. Since then, automorphic properties of various related combinatorial families have been studied. Here, extending work of Andrews and Bringmann, we study general infinite families of combinatorial q-series pertaining to k-marked Durfee symbols, in which we allow additional singularities. We show that these singular combinatorial families are essentially mixed mock and quasimock modular forms, and provide their explicit non-holomorphic completions. As a special case of our work, we consider k=3, and provide an asymptotic expansion for the associated partition rank statistic, solving a special case of an open problem of Andrews.},
author = {Amanda Folsom, Susie Kimport},
journal = {Acta Arithmetica},
keywords = {weak Maass forms; mock modular forms; non-holomorphic modular forms; integer partitions; partition ranks; generating functions},
language = {eng},
number = {3},
pages = {257-297},
title = {Mock modular forms and singular combinatorial series},
url = {http://eudml.org/doc/279233},
volume = {159},
year = {2013},
}

TY - JOUR
AU - Amanda Folsom
AU - Susie Kimport
TI - Mock modular forms and singular combinatorial series
JO - Acta Arithmetica
PY - 2013
VL - 159
IS - 3
SP - 257
EP - 297
AB - A celebrated result of Bringmann and Ono shows that the combinatorial rank generating function exhibits automorphic properties after being completed by the addition of a non-holomorphic integral. Since then, automorphic properties of various related combinatorial families have been studied. Here, extending work of Andrews and Bringmann, we study general infinite families of combinatorial q-series pertaining to k-marked Durfee symbols, in which we allow additional singularities. We show that these singular combinatorial families are essentially mixed mock and quasimock modular forms, and provide their explicit non-holomorphic completions. As a special case of our work, we consider k=3, and provide an asymptotic expansion for the associated partition rank statistic, solving a special case of an open problem of Andrews.
LA - eng
KW - weak Maass forms; mock modular forms; non-holomorphic modular forms; integer partitions; partition ranks; generating functions
UR - http://eudml.org/doc/279233
ER -