Results 11 to 20 of about 230 (149)
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.
花元, 誠一 +2 more
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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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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 $\Gamma_0 (N)$.
Treneer, Stephanie
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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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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
doaj +2 more sources
Zeros of weakly holomorphic modular forms of levels 2 and 3 [PDF]
Mathematical Research Letters, 2013 Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $Γ_0(N)$ that are holomorphic at all cusps except possibly at $\infty$. We study a canonical basis for $M_k^\sharp(2)$ and $M_k^\sharp(3)$ and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a ...
Garthwaite, Sharon, Jenkins, Paul
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Algebraic de Rham theory for weakly holomorphic modular forms of level one [PDF]
Algebra & Number Theory, 2018 We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. This leads to formulae for the periods and quasi-periods of modular forms.
Brown, Francis, Hain, Richard
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Zagier duality and integrality of Fourier coefficients for weakly holomorphic modular forms
Journal of Number Theory, 2015 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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A basis for the space of weakly holomorphic Drinfeld modular forms of level T
Journal of Number TheoryIn this article, we explicitly construct a canonical basis for the space of certain weakly holomorphic Drinfeld modular forms for $Γ_0(T)$ (resp., for $Γ_0^+(T)$) and compute the generating function satisfied by the basis elements. We also give an explicit expression for the action of the $Θ$-operator, which depends on the divisor of meromorphic ...
Tarun Dalal
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Basis for the space of weakly holomorphic modular forms in higher level cases
Journal of Number Theory, 2013 Let \(p\) be either \(1\) or a prime number. Let \(\Gamma_0(p)^+\) be the group generated by the group \(\Gamma_0(p)\) and the Fricke involution \(W_p\) and \(M_k^!(\Gamma_0(p)^+)\) be the space of weakly holomorphic modular forms (that is, meromorphic with poles only at the cusps) of even integral weight \(k\) with respect to \(\Gamma_0(p)^+\).
Soyoung Choi
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