Vector-valued higher depth quantum modular forms and higher Mordell integrals
arXiv:1803.06261
summary
The authors prove that vector‑valued functions arising from characters of certain vertex algebras satisfy higher‑depth quantum modular properties, and they represent the resulting modularity errors using two‑dimensional Mordell integrals.
Abstract
In this paper, we prove vector-valued higher depth quantum modular properties arising from characters of certain vertex algebras. We then find two-dimensional Mordell integral representations for their errors of modularity.
21 pages, to appear in Journal of Mathematical Analysis and Applications
Topics & keywords
#quantum modular forms#vector-valued modular forms#vertex algebras#Mordell integrals#higher depthhigher depthvector-valuedMordell integralvertex algebra charactersmodularity error