Twisted traces of singular moduli of weakly holomorphic modular functions

Details Twisted traces of singular moduli of weakly holomorphic modular functions Twisted traces of singular moduli of weakly holomorphic modular functions

2011-05-06

arxiv.org/abs/1105.1223v1

Mathematics

Number Theory

Scientific paper

Zagier proved that the generating series for the traces of singular moduli is a \textit{weakly holomorphic} modular form of weight 3/2 on $\Gamma_0(4)$. Bruinier and Funke extended the results of Zagier to modular curves of arbitrary genus. Zagier also showed that the twisted traces of singular moduli are generated by a weakly holomorphic modular form of weight 3/2. In this paper, we study the extension of Zagier's result for the twisted traces of singular moduli to congruence subgroups $\Gamma_0(N)$. As an application, we study congruences for the twisted traces of singular moduli of weakly holomorphic modular functions on $\Gamma_0(N)$.

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