A magnetic modular form
Number Theory
2018-09-19 v2
Abstract
In this paper, we prove a conjecture of Broadhurst and Zudilin \cite{BZ17} concerning a divisibility property of the Fourier coefficients of a meromorphic modular form using the generalization of the Shimura lift by Borcherds \cite{Borcherds98} and Hecke operators on vector-valued modular forms developed by Bruinier and Stein \cite{BS10}. Furthermore, we construct a family of meromorphic modular forms with this property.
Cite
@article{arxiv.1808.04157,
title = {A magnetic modular form},
author = {Yingkun Li and Michael Neururer},
journal= {arXiv preprint arXiv:1808.04157},
year = {2018}
}
Comments
Version 2 contains a new result, Theorem 1.5, and some minor changes