On Jacobi–Weierstrass mock modular forms

Advances in Mathematics, vol. 465, pp. 110147

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.

Authors 4

1. Claudia Alfes‐Neumann

   Bielefeld University

   Affiliation as printed

   Universität Bielefeld, Fakultät für Mathematik, Postfach 100 131, 33501 Bielefeld, Germany

2. Jens Funke

   Durham University

   Affiliation as printed

   Durham University, Department of Mathematical Sciences, Science Laboratories, South Rd, Durham DH1 3LE, United Kingdom

3. Michael H. Mertens Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Lehrstuhl für Algebra und Zahlentheorie, Pontdriesch 14/16, 52062 Aachen, Germany

4. Eugenia Rosu corresponding Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Leiden University, Mathematical Institute, Einsteinweg 55, 2333 CA Leiden, Netherlands