Asymptotic distribution of traces of singular moduli

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.

14 pages

References in corpus (1)

• Modular invariants for real quadratic fields and Kloosterman sums