Work

On Jacobi–Weierstrass mock modular forms

Year: 2025

Type: article

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.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110147

Authors: Claudia Alfes, Jens Funke, Michael H. Mertens, Eugenia Rosu

Institutions: Bielefeld University, Durham University, RWTH Aachen University, Leiden University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: Deutsche Forschungsgemeinschaft, Daimler und Benz Stiftung