Results 21 to 30 of about 205 (137)
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.
Seiichi Hanamoto
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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.
D. Doud, P. Jenkins
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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.
KATHRIN BRINGMANN +2 more
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Shimura lifts of weakly holomorphic modular forms [PDF]
Mathematische Zeitschrift, 2017 We show how to realize the Shimura lift of arbitrary level and character using the vector-valued theta lifts of Borcherds. Using the regularization of Borcherds' lift we extend the Shimura lift to take weakly holomorphic modular forms of half-integral weight to meromorphic modular forms of even integral weight having poles at CM points.
Yingkun Li, Shaul Zemel
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Divisibility properties for weakly holomorphic modular forms with sign vectors [PDF]
International Journal of Number Theory, 2016 In this paper, we prove some divisibility results for the Fourier coefficients of reduced modular forms with sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight [Formula: see text], which is related to the weight of Borcherds lifts when [Formula: see text].
Yichao Zhang
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Odd coefficients of weakly holomorphic modular forms [PDF]
Mathematical Research Letters, 2008 ). We will consider the question ofestimating the number of integers n for which a(n) 6≡0 (mod v).For a well-studied example, let p(n) be the ordinary partition function. Manyauthors have considered the problem of estimating the number of odd values of p(n).Among other references, one may see [1], [5], [15], [16], [17], [18], [19], [22], or [24].To see
Scott Ahlgren, Matthew Boylan
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Special $L$-values and periods of weakly holomorphic modular forms [PDF]
Proceedings of the American Mathematical Society, 2014 The authors study the special values of \(L\)-functions associated to weakly holomorphic modular forms; to define such an \(L\)-function, one makes use of appropriate regularization procedures. Let us cite a few of the authors': for \(f\in S^!_k\), where \(S^!_k\) denotes the space of weight \(k\) weakly holomorphic cusp forms, write \[ f(z)= \sum ...
Kathrin Bringmann +2 more
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Weakly holomorphic modular forms in prime power levels of genus zero [PDF]
, 2017 Let $M_k^\sharp(N)$ be the space of weight $k$, level $N$ weakly holomorphic modular forms with poles only at the cusp at $\infty$. We explicitly construct a canonical basis for $M_k^\sharp(N)$ for $N\in\{8,9,16,25\}$, and show that many of the Fourier coefficients of the basis elements in $M_0^\sharp(N)$ are divisible by high powers of the prime ...
Paul A. Jenkins, DJ Thornton
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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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Zagier duality for level p weakly holomorphic modular forms [PDF]
The 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 A. Jenkins, Grant Molnar
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