Results 101 to 110 of about 129 (113)

Zeros of weakly holomorphic modular forms of level 5

International Journal of Number Theory, 2016
Let [Formula: see text] be the space of weakly holomorphic modular forms of weight [Formula: see text] and level [Formula: see text] that are holomorphic away from the cusp at [Formula: see text]. We study a canonical basis for [Formula: see text] and the locations of zeros of this basis in a fundamental domain. We give a lower bound for the number of
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Arithmetic properties for the minus space of weakly holomorphic modular forms

Journal of Number Theory, 2019
Let \(M_k^{\prime}(p)\) (resp. \(M_k^{\prime\, +}(p)\)) be the space of weakly holomrorphic modular forms of weight \(k\) for the Hecke group \(\Gamma_0(p)\) (resp. \(\Gamma_0^+(p)=\) where \(W_p\) is the Fricke involution). Let \(M_k^{\prime\, -}(p)\) denote the minus subspace of \(M_k^{\prime}(p)\) consisting of all eigenfunctions of \(W_p\) with ...
SoYoung Choi, Chang Heon Kim, Kyung Seung Lee   +2 more
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On the zeros of certain weakly holomorphic modular forms for ${\varGamma }_0^+(5)$ and ${\varGamma }_0^+(7)$

Acta Arithmetica, 2021
Let \(p\) be \(1\) or a prime number. Let \(\Gamma_0^+(p)\) be the Fricke group generated by the Hecke group \(\Gamma_0(p)\) and the Fricke involution. Let \(M_k^!(\Gamma_0^+(p))\) be the space of weakly holomorphic modular forms of even weight \(k\). This space has a natural basis \(\{f_{k,m}\}_{m\ge m_{p,k}}\) such that \(f_{k,m}(z)=q^{-m}+O(q^{m_{p ...
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Effective bounds for Fourier coefficients of certain weakly holomorphic modular forms

Journal of Number Theory, 2018
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DIVISIBILITY PROPERTIES OF COEFFICIENTS OF WEIGHT 0 WEAKLY HOLOMORPHIC MODULAR FORMS

International Journal of Number Theory, 2011
In 1949, Lehner showed that certain coefficients of the modular invariant j(τ) are divisible by high powers of small primes. Kolberg refined Lehner's results and proved congruences for these coefficients modulo high powers of these primes. We extend Lehner's and Kolberg's work to the elements of a canonical basis for the space of weight 0 weakly ...
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A family of weakly holomorphic modular forms for $\Gamma _0(2)$ with all zeros on a certain geodesic

Acta Arithmetica, 2019
Let \(M^!_K (\Gamma_0 (2))\) be the space of weakly holomorphic modular forms of weight \(k\) for \(\Gamma_0 (2)\), and let \(M^{!-}_K (\Gamma_0 (2))\) the subspace consisting of elements \(f \in M^!_K (\Gamma_0 (2))\) with \(f \mid_k \left(\begin{smallmatrix} 0& -1/\sqrt{2} \\ \sqrt{2} & 0 \end{smallmatrix}\right) = -f\).
Choi, Soyoung, Im, Bo-Hae
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Generalized Hecke operators on weakly holomorphic modular forms of non-positive weight

International Journal of Number Theory
Generalized Hecke operators, originating from the replication formula in Monstrous Moonshine, were extended in [D. Jeon, S.-Y. Kang and C. H. Kim, The Hecke system of harmonic Maass functions and applications to modular curves of higher genera Ramanujan J.
Chang Heon Kim, Kyeong Seok Min
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The transcendence of zeros of natural basis elements for the space of the weakly holomorphic modular forms for $\Gamma_{0}^{+}(3)$

Proceedings of the Japan Academy Series A: Mathematical Sciences, 2022
Soyoung Choi
exaly  

Interlacing of zeros of certain weakly holomorphic modular forms for Γ0+(2)

Journal of Mathematical Analysis and Applications, 2017
Bo-Hae Im, Soyoung Choi
exaly  

$p$-adic properties of coefficients of basis for the space of weakly holomorphic modular forms of weight 2

Proceedings of the Japan Academy Series A: Mathematical Sciences, 2012
Soyoung Choi
exaly