A family of vector-valued quantum modular forms of depth two
Number Theory
2020-09-14 v2
Abstract
We introduce and investigate an infinite family of functions which are shown to have generalised quantum modular properties. We realise their "companions" in the lower half plane both as double Eichler integrals and as non-holomorphic theta functions with coefficients given by double error functions. Further, we view these Eichler integrals in a modular setting as parts of certain weight two indefinite theta series.
Keywords
Cite
@article{arxiv.1810.01341,
title = {A family of vector-valued quantum modular forms of depth two},
author = {Joshua Males},
journal= {arXiv preprint arXiv:1810.01341},
year = {2020}
}
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33 pages