Results 21 to 30 of about 129 (113)
On cycle integrals of weakly holomorphic modular forms [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2015 AbstractIn this paper, we investigate cycle integrals of weakly holomorphic modular forms. We show that these integrals coincide with the cycle integrals of classical cusp forms. We use these results to define a Shintani lift from integral weight weakly holomorphic modular forms to half-integral weight holomorphic modular forms.
Bringmann, Kathrin +2 more
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ZEROS OF CERTAIN WEAKLY HOLOMORPHIC MODULAR FORMS
Kyushu Journal of Mathematics, 2023 Summary: Weakly holomorphic modular forms for modular groups are holomorphic away from the cusp. We study a certain family of weakly holomorphic modular forms and the locations of their zeros. We prove that all of the zeros in the standard fundamental domain for the modular group lie on a lower boundary arc, providing conditions.
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Congruences involving the $$U_{\ell }$$ operator for weakly holomorphic modular forms [PDF]
The Ramanujan Journal, 2019 Let $λ$ be an integer, and $f(z)=\sum_{n\gg-\infty} a(n)q^n$ be a weakly holomorphic modular form of weight $λ+\frac 12$ on $Γ_0(4)$ with integral coefficients. Let $\ell\geq 5$ be a prime. Assume that the constant term $a(0)$ is not zero modulo $\ell$.
Choi, Dohoon, Lim, Subong
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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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Linear relations between modular forms for Г0+(p)
Open Mathematics, 2015 We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.
Choi SoYoung, Kim Chang Heon
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On the algebraicity of coefficients of half-integral weight mock modular forms
Open Mathematics, 2018 Extending works of Ono and Boylan to the half-integral weight case, we relate the algebraicity of Fourier coefficients of half-integral weight mock modular forms to the vanishing of Fourier coefficients of their shadows.
Choi SoYoung, Kim Chang Heon
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Rank generating functions as weakly holomorphic modular forms [PDF]
Acta Arithmetica, 2008 We study infinite families of generating functions involving the rank of the ordinary partition function, which include as special cases many of the generating functions introduced by Atkin and Swinnerton-Dyer in the 1950s. We prove that each of these generating functions is a weakly holomorphic modular form of weight 1/2 on some congruence subgroup Γ1(
Scott Ahlgren, Stephanie Treneer
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Zeros of certain weakly holomorphic modular forms for the Fricke group ${\varGamma }_0^+(3)$
Acta Arithmetica, 2021 19 ...
Hanamoto, Seiichi, Kuga, Seiji
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Open Mathematics, 2019 After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
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CONGRUENCES FOR THE COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS [PDF]
Proceedings of the London Mathematical Society, 2006 Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomenon is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup $\Gamma_0 (N)$.
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