The Hecke system of harmonic Maass functions and applications to modular curves of higher genera

Jeon, Daeyeol; Kang, Soon-Yi; Kim, Chang Heon

doi:10.1007/s11139-022-00689-8

Cited by 3 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ahlgren [1,Theorem 3] generalized this result to Γ 0 (p) for p ∈ {2, 3, 5, 7, 13}. In [7, Theorem 3.2] and [18,Theorem 1.1], they showed that similar results hold for Γ + 0 (p)(which is the subgroup of PSL 2 (R) generated by Γ 0 (p) and Atkin-Lehner involution W p = 0 −1 p 0 ) when p ∈ {2, 3,5,7,11,13,17,19,23,29,31,41,47, 59, 71}. For example, in [18,Theorem 1.1], they showed that if the genus of X + 0 (N ) is zero, then…”

Section: Introductionmentioning

confidence: 84%

See 1 more Smart Citation

Algebraicity of weakly holomorphic modular functions at divisors of meromorphic modular forms for certain Fuchsian groups

Kim,

Shin

2024

Preprint

Self Cite

View full text Add to dashboard Cite

We show that the values of a certain basis of weakly holomorphic modular functions on $\Gamma_{0}^{+}(N)$ at points of the divisors of any meromorphic modular form of weight $k$ on $\Gamma_{0}^{+}(N)$ with algebraic Fourier coefficients are algebraic. We also find the basis of an Eisenstein space of weight 2 on $\Gamma_{0}^{+}(N)$. As an application, we show that a certain eta quotient has only single zeros on the fundamental domain. Moreover, we give a number field containing all the values of the certain basis of $M_{0}^{\#}(\G)$ at the zeros of this certain eta quotient. 2010 Mathematics Subject Classification: 11F03, 11F12, 11F25, 11F30, 11G30, 11R04

show abstract

Section: Introductionmentioning

confidence: 84%

“…for each n ≥ −g, where g is the genus of X(Γ). In [13], they established that the duality condition between the Fourier coefficients of f Γ,m (τ ) and g Γ,n (τ ) is given by the following equation:…”

Section: Introductionmentioning

confidence: 99%