Hecke operators for weakly holomorphic modular forms and supersingular congruences [PDF]
We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.
Pavel Guerzhoy
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Congruences involving the $U_{\ell}$ operator for weakly holomorphic modular forms [PDF]
Let $ $ be an integer, and $f(z)=\sum_{n\gg-\infty} a(n)q^n$ be a weakly holomorphic modular form of weight $ +\frac 12$ on $ _0(4)$ with integral coefficients. Let $\ell\geq 5$ be a prime. Assume that the constant term $a(0)$ is not zero modulo $\ell$. Further, assume that, for some positive integer $m$, the Fourier expansion of $(f|U_{\ell^m})(z) =
Dohoon Choi, Subong Lim
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Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras
In this paper, we compute basis elements of certain spaces of weight 0 0 weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the rank 2 2 hyperbolic Kac-Moody algebras H
Henry Kim, Kyu‐Hwan Lee, Yichao Zhang
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Hecke grids and congruences for weakly holomorphic modular forms
Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain residue classes, and conjectured the existence of similar congruences modulo higher powers of $p$. Partial results
Scott Ahlgren, Nickolas Andersen
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$p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral Weight
Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on $ _{0}(4N)$ for $N=1,2,4$.
Dohoon Choi, YoungJu Choie
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The transcendence of zeros of natural basis elements for the space of the weakly holomorphic modular forms for $\Gamma_{0}^{+}(3)$ [PDF]
Soyoung Choi
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Divisibility properties for weakly holomorphic modular forms with sign vectors [PDF]
In this paper, we prove some divisibility results for the Fourier coefficients of reduced modular forms with sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight [Formula: see text], which is related to the weight of Borcherds lifts when [Formula: see text].
Yichao Zhang
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Hecke structures of weakly holomorphic modular forms and their algebraic properties
Abstract Let S k ! ( Γ 1 ( N ) ) be the space of weakly holomorphic cusp forms of weight k on Γ 1 ( N ) with an even integer k > 2 and M k ! ( Γ 1 ( N ) ) be the space of weakly holomorphic modular forms of weight k on Γ 1 ( N ) .
Subong Lim, Dohoon Choi
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$p$-adic properties of coefficients of basis for the space of weakly holomorphic modular forms of weight 2 [PDF]
We observe properties of coefficients of certain basis elements for the space of weakly holomorphic modular forms of weight 2 for $SL_{2}(\mathbf{Z})$. Moreover we show that these coefficients are often highly divisible by the primes 2, 3, 5, 7, 11.
Soyoung Choi
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Hecke grids and congruences for weakly holomorphic modular forms [PDF]
Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain residue ...
Scott Ahlgren, Nickolas Andersen
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