Abstract
Let p be a prime and f(z)=∑ n a(n)q n be a weakly holomorphic modular function for \(\varGamma _{0}^{*}(p^{2})\) with a(0)=0. We use Bruinier and Funke’s work to find the generating series of modular traces of f(z) as Jacobi forms. And as an application we construct Borcherds products related to the Hauptmoduln \(j_{p^{2}}^{*}\) for genus zero groups \(\varGamma _{0}^{*}(p^{2})\).
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This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (2009-0063182).
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Kim, C.H. The generating function for traces of singular moduli and an application to Borcherds products. Ramanujan J 22, 187–207 (2010). https://doi.org/10.1007/s11139-009-9196-7
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DOI: https://doi.org/10.1007/s11139-009-9196-7