A magnetic modular form

Yingkun Li; Michael Neururer

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arXiv · 1808.04157

A magnetic modular form

Yingkun Li·Michael Neururer

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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.

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Yingkun Li, Michael Neururer. 2018-08-13. A magnetic modular form. https://arxiv.org/abs/1808.04157

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