On Jacobi–Weierstrass mock modular forms

Alfes, Claudia; Funke, Jens; Mertens, Michael H; Rosu, Eugenia

Abstract

We construct harmonic weak Maass forms that map to cusp forms of weight k ≥ 2 with rational coefficients under the ξ-operator. This generalizes work of the first author, Griffin, Ono, and Rolen, who constructed distinguished preimages under this differential operator of weight 2 newforms associated to rational elliptic curves using the classical Weierstrass theory of elliptic functions. We extend this theory and construct a vector-valued Jacobi–Weierstrass ζ-function which is a generalization of the classical Weierstrass ζ-function.

Citation

Alfes, C., Funke, J., Mertens, M. H., & Rosu, E. (2025). On Jacobi–Weierstrass mock modular forms. Advances in Mathematics, 465, Article 110147. https://doi.org/10.1016/j.aim.2025.110147

• Journal Article Type: Article
• Acceptance Date: Feb 1, 2025
• Online Publication Date: Feb 19, 2025
• Publication Date: 2025-04
• Deposit Date: Feb 5, 2025
• Publicly Available Date: Feb 25, 2025
• Journal: Advances in Mathematics
• Print ISSN: 0001-8708
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 465
• Article Number: 110147
• DOI: https://doi.org/10.1016/j.aim.2025.110147
• Public URL: https://durham-repository.worktribe.com/output/3468961