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Effective estimates for traces of singular moduli
- Source :
- Research in Number Theory, 10, 29 (2024)
- Publication Year :
- 2023
-
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 $\Gamma_0(4)$.
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Research in Number Theory, 10, 29 (2024)
- Publication Type :
- Report
- Accession number :
- edsarx.2305.19649
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s40993-024-00517-6