2023/03/02 by Alfes-Neumann, Claudia, Funke, Jens, Mertens, Michael +1
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2303.01445
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.