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arXiv · 2305.19649

Effective estimates for traces of singular moduli

Oscar E. González·Qihang Sun
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Abstract

Traces of singular moduli can be approximated by exponential sums of quadratic irrationals. Recently Andersen and Duke used theory of Maass forms to estimate generalized twisted traces with power-saving error bounds. We establish an asymptotic formula with effective error bounds for such traces. Our methods depend on an explicit bound for sums of Kloosterman sums on $\Gamma_0(4)$.

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Oscar E. González, Qihang Sun. 2023-05-31. Effective estimates for traces of singular moduli. https://doi.org/10.1007/s40993-024-00517-6

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