Arithmetic Properties of Traces of Singular Moduli on Congruence Subgroups

2009/04/24 by Soon-Yi Kang, Kang, Soon-Yi, Chang Heon Kim +1
Mathematics · #11F03 #11F30 #11F37 #Advanced Harmonic Analysis Research #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0904.3777

openalex publication_date 2009/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After Zagier proved that the traces of singular moduli j(z) are Fourier coefficients of a weakly holomorphic modular form, various properties of the traces of the singular values of modular functions mostly on the full modular group PSL₂(ℤ) have been investigated such as their exact formulas, limiting distribution, duality, and congruences. The purpose of this paper is to generalize these arithmetic properties of traces of singular values of a weakly holomorphic modular function on the full modular group to those on a congruence subgroup Γ₀(N).

Citations

• Arithmetic properties of coefficients of half-integral weight Maass–Poincaré series

Related

• Twisted traces of singular moduli of weakly holomorphic modular functions
• Exact formulas for traces of singular moduli of higher level modular functions
• On Traces of Singular Moduli
• Traces of CM values of modular functions
• Traces of singular values and Borcherds products