Vol. 2, No. 5, 2008

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Integral traces of singular values of weak Maass forms

William Duke and Paul Jenkins

Vol. 2 (2008), No. 5, 573–593
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 coefficients of certain weakly holomorphic forms of half-integral weight. If the coefficients 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
Primary: 11F30
Secondary: 11F37