Asymptotic distribution of traces of singular moduli

preprint2022arXivOpen access

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∞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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