Quantum Modular Forms from Real Quadratic Double Sums
Number Theory
2023-04-13 v3
Abstract
In 2015, Lovejoy and Osburn discovered twelve -hypergeometric series and proved that their Fourier coefficients can be understood as counting functions of ideals in certain quadratic fields. In this paper, we study their modular and quantum modular properties and show that they yield three vector-valued quantum modular forms on the group .
Keywords
Cite
@article{arxiv.2205.02643,
title = {Quantum Modular Forms from Real Quadratic Double Sums},
author = {Kathrin Bringmann and Caner Nazaroglu},
journal= {arXiv preprint arXiv:2205.02643},
year = {2023}
}
Comments
26 pages; v2: Brief comments added. To appear in the Quarterly Journal of Mathematics. v3: Incomplete funding information corrected