Zeros of weakly holomorphic modular forms of level 4 [PDF]
International Journal of Number Theory, 2013 Let [Formula: see text] be the space of weakly holomorphic modular forms of weight k and level 4 that are holomorphic away from the cusp at ∞. We define a canonical basis for this space and show that for almost all of the basis elements, the majority of their zeros in a fundamental domain for Γ0(4) lie on the lower boundary of the fundamental domain ...
A. Glen Haddock, Paul M. Jenkins
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Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2014 AbstractWe prove that the coefficients of the mock theta functions \begin{eqnarray*} f(q) = \sum_{n=1}^{\infty} \frac{ q^{n^2}}{(1+q)^2 (1+q^2)^2 \cdots (1+q^n)^2 } \end{eqnarray*} and \begin{eqnarray*} \omega(q)=1+\sum_{n=1}^\infty \frac{q^{2n^2+2n}}{(1+q)^2(1+q^3)^2\cdots (1+q^{2n+1})^2} \end{eqnarray*} possess no linear congruences modulo 3.
SCOTT AHLGREN, BYUNGCHAN KIM
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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 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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$p$-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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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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Zeros of weakly holomorphic modular forms of levels 2 and 3 [PDF]
Mathematical Research Letters, 2013 Added a reference, corrected ...
Sharon Anne Garthwaite, Paul M. Jenkins
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Two-divisibility of the coefficients of certain weakly holomorphic modular forms [PDF]
The Ramanujan Journal, 2012 We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly ...
Darrin Doud +2 more
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Zeros of certain weakly holomorphic modular forms for the Fricke group ${\varGamma }_0^+(3)$
Acta Arithmetica, 2021 Comment: 19 ...
Hanamoto, Seiichi, Kuga, Seiji
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