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Half-integral weight p-adic coupling of weakly holomorphic and holomorphic modular forms [PDF]
Research in Number Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kathrin Bringmann +2 more
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Congruences involving the $U_{\\ell}$ operator for weakly holomorphic\n modular forms [PDF]
The Ramanujan Journal, 2019 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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Odd coefficients of weakly holomorphic modular forms [PDF]
Mathematical Research Letters, 2008 ). We will consider the question ofestimating the number of integers n for which a(n) 6≡0 (mod v).For a well-studied example, let p(n) be the ordinary partition function. Manyauthors have considered the problem of estimating the number of odd values of p(n).Among other references, one may see [1], [5], [15], [16], [17], [18], [19], [22], or [24].To see
Scott Ahlgren, Matthew Boylan
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Special $L$-values and periods of weakly holomorphic modular forms [PDF]
Proceedings of the American Mathematical Society, 2014 The authors study the special values of \(L\)-functions associated to weakly holomorphic modular forms; to define such an \(L\)-function, one makes use of appropriate regularization procedures. Let us cite a few of the authors': for \(f\in S^!_k\), where \(S^!_k\) denotes the space of weight \(k\) weakly holomorphic cusp forms, write \[ f(z)= \sum ...
Kathrin Bringmann +2 more
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Divisibility properties for weakly holomorphic modular forms with sign vectors [PDF]
International Journal of Number Theory, 2016 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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Zagier duality and integrality for Fourier coefficients for weakly holomorphic modular forms [PDF]
Journal of Number Theory, 2013 Worked out the isomorphisms for a general sign vector; proved Zagier duality for canonical bases; raise a question on integrality; 24 ...
Yichao Zhang
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Hecke operators for weakly holomorphic modular forms and supersingular congruences [PDF]
Proceedings of the American Mathematical Society, 2008 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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Weakly holomorphic modular forms for some moonshine groups [PDF]
Archiv der Mathematik, 2014 In an article in the Pure and Applied Mathematics Quarterly in 2008, Duke and Jenkins investigated a certain natural basis of the space of weakly holomorphic modular forms for the full modular group $SL_2({\bf Z})$. We show here that their results can be generalized to certain moonshine groups, also allowing characters that are real on the underlying ...
Martina Lahr, Rainer Schulze‐Pillot
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$p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral Weight [PDF]
, 2007 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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On the Zeros and Coefficients of Certain Weakly Holomorphic Modular Forms [PDF]
Pure and Applied Mathematics Quarterly, 2008 A \textit{weakly holomorphic modular form} (say, \(f\)) of weight \(k\in 2\mathbb{Z}\) for the full modular group \(\mathrm{PSL}_{2}(\mathbb{Z})\) is defined the same way as holomorphic modular form, only \(f\) is allowed to have a finite number of negative powers in its \(q\)-expansion. Write \(k=12\ell+k'\) with uniquely determined \(\ell\in\mathbb{Z}
William Duke, Paul A. Jenkins
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