Interlacing of zeros of weakly holomorphic modular forms [PDF]
Proceedings of the American Mathematical Society, Series B, 2014 We prove that the zeros of a family of extremal modular forms interlace, settling a question of Nozaki. Additionally, we show that the zeros of almost all forms in a basis for the space of weakly holomorphic modular forms of
Paul Jenkins, Kyle Pratt
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Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms
Open Mathematics, 2022 Extending our previous work we construct weakly holomorphic Hecke eigenforms whose period polynomials correspond to elements in a basis consisting of odd and even Hecke eigenpolynomials induced by only cusp forms.
Choi SoYoung, Kim Chang Heon
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On the zeros of weakly holomorphic modular forms [PDF]
Archiv Der Mathematik, 2014 In this article, we study the nature of zeros of weakly holomorphic modular forms. In particular, we prove results about transcendental zeros of modular forms of higher levels and for certain Fricke groups which extend a work of Kohnen. Furthermore, we investigate the algebraic independence of values of weakly holomorphic modular forms.
Sanoli Gun +2 more
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Zagier duality for level p weakly holomorphic modular forms [PDF]
Ramanujan Journal, 2018 We prove Zagier duality between the Fourier coefficients of canonical bases for spaces of weakly holomorphic modular forms of prime level $p$ with $11 \leq p \leq 37$ with poles only at the cusp at $\infty$, and special cases of duality for an infinite class of prime levels. We derive generating functions for the bases for genus 1 levels.
Paul Jenkins +2 more
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p-Adic Properties of Coefficients of Weakly Holomorphic Modular Forms [PDF]
International Mathematics Research Notices, 2010 We examine the Fourier coefficients of modular forms in a canonical basis for the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coefficients are often highly divisible by the primes 2, 3, and 5.
Paul Jenkins, Jenkins Paul
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On values of weakly holomorphic modular functions at divisors of meromorphic modular forms [PDF]
Journal of Number Theory, 2022 We show that the values of a certain family of weakly holomorphic modular functions at points in the divisors of any meromorphic modular form with algebraic Fourier coefficients are algebraic. We use this to extend the classical result of Schneider by proving that zeros or poles of any non-zero meromorphic modular form with algebraic Fourier ...
Daeyeol Jeon +2 more
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Weakly holomorphic modular forms for some moonshine groups [PDF]
Archiv Der Mathematik, 2014 Some misprints corrected.
Rainer Schulze-Pillot +1 more
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Half-integral weight p-adic coupling of weakly holomorphic and holomorphic modular forms [PDF]
Research in Number Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kathrin Bringmann +2 more
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Two-divisibility of the coefficients of certain weakly holomorphic modular forms [PDF]
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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Hecke structures of weakly holomorphic modular forms and their algebraic properties
Journal of Number Theory, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dohoon Choi, Subong Lim
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