On Kleinian mock modular forms

Research in the Mathematical Sciences, vol. 11

Abstract

Abstract We give an explicit and computationally efficient construction of harmonic weak Maass forms which map to weight 2 newforms under the $$\xi $$ ξ -operator. Our work uses a new non-analytic completion of the Kleinian $$\zeta $$ ζ -function from the theory of Abelian functions.

Authors 2

1. Claudia Alfes‐Neumann

   Bielefeld University

   Affiliation as printed

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

2. Michael H. Mertens corresponding Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

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