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. (in press). ON JACOBI-WEIERSTRASS MOCK MODULAR FORMS. Advances in Mathematics,

• Journal Article Type: Article
• Acceptance Date: Feb 1, 2025
• Deposit Date: Feb 5, 2025
• Journal: Advances in Mathematics
• Print ISSN: 0001-8708
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Public URL: https://durham-repository.worktribe.com/output/3468961
• Publisher URL: https://www.sciencedirect.com/journal/advances-in-mathematics