Work

On Jacobi--Weierstrass mock modular forms

Year: 2023

Type: preprint

Abstract: We construct harmonic weak Maass forms that map to cusp forms of weight $k\geq 2$ 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: arXiv (Cornell University)

DOI: 10.48550/arxiv.2303.01445

Authors: Alfes-Neumann, Claudia, Funke, Jens, Mertens, Michael, Rosu, Eugenia

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Daimler und Benz Stiftung

Awards: G6601682123, TRR 358: Ganzzahlige Strukturen in Geometrie und Darstellungstheorie, TRR 326: Geometrie und Arithmetik uniformisierter Strukturen (GAUS)

OpenAlex ID: W4323076537

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