Twisted Traces of CM values of Harmonic Weak Maass Forms
Claudia Alfes, Stephan Ehlen
TL;DR
This paper demonstrates that twisted traces of CM values of weak Maass forms of weight 0 are Fourier coefficients of vector valued weak Maass forms of weight 3/2, extending Zagier's work on singular moduli.
Contribution
It introduces a twisted theta lift approach to relate CM value traces of weak Maass forms to vector valued forms, generalizing previous results.
Findings
Twisted traces correspond to Fourier coefficients of vector valued weak Maass forms.
The approach generalizes Zagier's work on singular moduli.
Utilizes a twisted theta lift by Bruinier and Funke.
Abstract
We show that the twisted traces of CM values of weak Maass forms of weight 0 are Fourier coefficients of vector valued weak Maass forms of weight 3/2. These results generalize work by Zagier on traces of singular moduli. We utilize a twisted version of the theta lift considered by Bruinier and Funke.
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