Vector-valued higher depth quantum modular forms and higher Mordell integrals

TL;DR

This paper establishes vector-valued higher depth quantum modular properties from vertex algebra characters and derives two-dimensional Mordell integral representations for their modularity errors.

Contribution

It introduces new vector-valued higher depth quantum modular forms and connects them to Mordell integrals, advancing understanding of modularity in vertex algebra contexts.

Findings

Proved vector-valued higher depth quantum modular properties.

Derived Mordell integral representations for modularity errors.

Linked quantum modular forms to vertex algebra characters.

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.