Effective estimates for traces of singular moduli

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...

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Bibliographic Details
Published in:Research in number theory 2024-06, Vol.10 (2), Article 29
Main Authors: González, Oscar E., Sun, Qihang
Format: Article
Language:English
Subjects:
Asymptotic methods
Mathematics
Mathematics and Statistics
Number Theory
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Summary: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 Γ 0 ( 4 ) .
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-024-00517-6