Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras [PDF]
Transactions of the American Mathematical Society, 2015 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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Algebraicity of weakly holomorphic modular functions at divisors of meromorphic modular forms for certain Fuchsian groups [PDF]
Abstract 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 $\Gamma_{0}^{+}(N)$.
Chang Heon Kim, Gyucheol Shin
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Quadratic Chabauty for Atkin-Lehner quotients of modular curves via weakly holomorphic modular forms: Hodge Filtrations [PDF]
32 pages, comments ...
Isabel Rendell
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Weakly holomorphic modular forms of half-integral weight with nonvanishing constant terms modulo $\ell $ [PDF]
Transactions of the American Mathematical Society, 2009 Summary: Let \( \ell\) be a prime and \( \lambda,j\geq 0\) be an integer. Suppose that \( f(z)=\sum_{n}a(n)q^n\) is a weakly holomorphic modular form of weight \( \lambda+\frac{1}{2}\) and that \( a(0)\not \equiv 0 \pmod{\ell}\). We prove that if the coefficients of \( f(z)\) are not ``well-distributed'' modulo \( \ell^j\), then \[ \lambda=0\text{ or }
Dong‐Soo Choi
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L-Series for Vector-Valued Weakly Holomorphic Modular Forms and Converse Theorems [PDF]
Canadian Journal of MathematicsAbstract We introduce the L-series of weakly holomorphic modular forms using Laplace transforms and give their functional equations. We then determine converse theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and elliptic modular forms of half-integral weight in Kohnen plus space.
Subong Lim, Wissam Raji
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Curves on K3 surfaces in divisibility 2
Forum of Mathematics, Sigma, 2021 We prove a conjecture of Maulik, Pandharipande and Thomas expressing the Gromov–Witten invariants of K3 surfaces for divisibility 2 curve classes in all genera in terms of weakly holomorphic quasi-modular forms of level 2.
Younghan Bae, Tim-Henrik Buelles
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4-manifolds and topological modular forms
Journal of High Energy Physics, 2021 We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds.
Sergei Gukov +3 more
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Shintani lifts and fractional derivatives for harmonic weak Maass forms [PDF]
, 2014 In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms.
Bringmann, Kathrin +2 more
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Sign-Periodicity of Traces of Singular Moduli
Mathematics, 2013 Zagier proved that the generating functions of traces of singular values of Jm(z) are weight 3/2 weakly holomorphic modular forms. In this paper we prove that there is the sign-periodicity of traces of singular values of Jm(z).
Subong Lim, Dohoon Choi, Byungchan Kim
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Regularized inner products and weakly holomorphic Hecke eigenforms [PDF]
, 2017 We show that the image of repeated differentiation on weak cusp forms is precisely the subspace which is orthogonal to the space of weakly holomorphic modular forms.
Bringmann, Kathrin, Kane, Ben
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