A magnetic modular form
Abstract
In this paper, we prove a conjecture of Broadhurst and Zudilin BZ17 concerning a divisibility property of the Fourier coefficients of a meromorphic modular form using the generalization of the Shimura lift by Borcherds Borcherds98 and Hecke operators on vector-valued modular forms developed by Bruinier and Stein BS10. Furthermore, we construct a family of meromorphic modular forms with this property.
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