English

Effective estimates for traces of singular moduli

Number Theory 2025-04-15 v1

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 Γ0(4)\Gamma_0(4).

Keywords

Cite

@article{arxiv.2305.19649,
  title  = {Effective estimates for traces of singular moduli},
  author = {Oscar E. González and Qihang Sun},
  journal= {arXiv preprint arXiv:2305.19649},
  year   = {2025}
}
R2 v1 2026-06-28T10:51:42.613Z