Results 121 to 130 of about 156 (139)

Three-divisibility of Fourier coefficients of weakly holomorphic modular forms

Ramanujan Journal, 2015
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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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ARITHMETIC OF WEAKLY HOLOMORPHIC MODULAR FORMS FOR HECKE GROUPS

JP Journal of Algebra, Number Theory and Applications, 2015
Summary: \textit{W. Duke} and \textit{P. Jenkins} [Pure Appl. Math. Q. 4, No. 4, 1327--1340 (2008; Zbl 1200.11027)] constructed a nice canonical basis for the space of weakly holomorphic modular forms of weight \(k\) for \(\mathrm{SL}_2(\mathbb{Z})\) that are holomorphic away from the cusp at infinity.
Ahn, Jaehyun, Choi, Soyoung
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The zeros of certain weakly holomorphic Drinfeld modular forms

Manuscripta Mathematica, 2014
Duke and Jenkins (Pure Appl Math Q 4(4):1327–1340, 2008) constructed a canonical basis for the space of weakly holomorphic modular forms for $${{\rm SL}_2(\mathbb{Z})}$$ and investigated the zeros of the ...
SoYoung Choi, Bo-Hae Im
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A basis for the space of weakly holomorphic Drinfeld modular forms for GL2(A)

Journal of Number Theory, 2022
Abstract We construct a canonical basis for the space of weakly holomorphic Drinfeld modular forms. And we find that the basis elements satisfy a generating function and the duality among coefficients of the basis elements. Moreover we obtain the congruence properties of t-expansion coefficients of these functions under some conditions.
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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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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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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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Effective bounds for Fourier coefficients of certain weakly holomorphic modular forms

Journal of Number Theory, 2018
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