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arXiv · 2011.02064

Asymptotic distribution of traces of singular moduli

Nickolas Andersen·William Duke
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Abstract

We determine the asymptotic behavior of twisted traces of singular moduli with a power-saving error term in both the discriminant and the order of the pole at $i\infty$. Using this asymptotic formula, we obtain an exact formula for these traces involving the class number and a finite sum involving the exponential function evaluated at CM points.

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Nickolas Andersen, William Duke. 2020-11-03. Asymptotic distribution of traces of singular moduli. https://doi.org/10.19086/da.33153

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