Geodesic
Mock modular forms and singular combinatorial series
Amanda Folsom 1   ; Susie Kimport 1
1 Mathematics Department Yale University 10 Hillhouse Avenue P.O. Box 208283 New Haven, CT 06520-8283, U.S.A.
Acta Arithmetica, Tome 159 (2013) no. 3, pp. 257-297 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/aa159-3-4
Keywords: celebrated result bringmann ono shows combinatorial rank generating function exhibits automorphic properties after being completed addition non holomorphic integral since automorphic properties various related combinatorial families have studied here extending work andrews bringmann study general infinite families combinatorial q series pertaining k marked durfee symbols which allow additional singularities these singular combinatorial families essentially mixed mock quasimock modular forms provide their explicit non holomorphic completions special work consider provide asymptotic expansion associated partition rank statistic solving special problem andrews

Amanda Folsom  1   ; Susie Kimport  1

1 Mathematics Department Yale University 10 Hillhouse Avenue P.O. Box 208283 New Haven, CT 06520-8283, U.S.A. 
@article{10_4064_aa159_3_4,
     author = {Amanda Folsom and Susie Kimport},
     title = {Mock modular forms and singular combinatorial series},
     journal = {Acta Arithmetica},
     pages = {257--297},
     year = {2013},
     volume = {159},
     number = {3},
     doi = {10.4064/aa159-3-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa159-3-4/}
}
TY  - JOUR
AU  - Amanda Folsom
AU  - Susie Kimport
TI  - Mock modular forms and singular combinatorial series
JO  - Acta Arithmetica
PY  - 2013
SP  - 257
EP  - 297
VL  - 159
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa159-3-4/
DO  - 10.4064/aa159-3-4
LA  - en
ID  - 10_4064_aa159_3_4
ER  - 
%0 Journal Article
%A Amanda Folsom
%A Susie Kimport
%T Mock modular forms and singular combinatorial series
%J Acta Arithmetica
%D 2013
%P 257-297
%V 159
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/aa159-3-4/
%R 10.4064/aa159-3-4
%G en
%F 10_4064_aa159_3_4
Amanda Folsom; Susie Kimport. Mock modular forms and singular combinatorial series. Acta Arithmetica, Tome 159 (2013) no. 3, pp. 257-297. doi: 10.4064/aa159-3-4

Cité par Sources :