English

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.

Keywords

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

R2 v1 2026-06-23T03:31:54.150Z