Abstract

We define traces associated to a weakly holomorphic modular form f of arbitrary negative even integral weight and show that these traces appear as coeficients of certain weakly holomorphic forms of half-integral weight. If the coeficients of f are integral, then these traces are integral as well. We obtain a negative weight analogue of the classical Shintani lift and give an application to a generalization of the Shimura lift.

Keywords

weak Maass forms, weakly holomorphic modular forms, traces of singular moduli

Mathematical Subject Classification

Primary: 11F30

Secondary: 11F37

Authors