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ZEROS OF CERTAIN WEAKLY HOLOMORPHIC MODULAR FORMS

open access: yesZEROS OF CERTAIN WEAKLY HOLOMORPHIC MODULAR FORMS
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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Algebraicity of weakly holomorphic modular functions at divisors of meromorphic modular forms for certain Fuchsian groups

open access: yes
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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Quantum geometry and mock modularity

open access: yes
International audienceIn previous work, we used new mathematical relations between Gopakumar-Vafa (GV) invariants and rank 0 Donaldson-Thomas (DT) invariants to determine the first few terms in the generating series of Abelian D4-D2-D0 indices for a ...
Pioline, Boris   +3 more
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Harmonic weak Maass forms and periods II. [PDF]

open access: yesMath Ann
Alfes C, Bruinier JH, Schwagenscheidt M.
europepmc   +1 more source

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