Results 21 to 30 of about 230 (149)
A note on congruences for weakly holomorphic modular forms [PDF]
Proceedings of the American Mathematical Society, 2021 Let O L O_L be the ring of integers of ...
Dembner, Spencer, Jain, Vanshika
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Curves on K3 surfaces in divisibility 2
Forum of Mathematics, Sigma, 2021 We prove a conjecture of Maulik, Pandharipande and Thomas expressing the Gromov–Witten invariants of K3 surfaces for divisibility 2 curve classes in all genera in terms of weakly holomorphic quasi-modular forms of level 2.
Younghan Bae, Tim-Henrik Buelles
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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.
Li, Yingkun, Zemel, Shaul
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ZEROS OF WEAKLY HOLOMORPHIC MODULAR FORMS OF LEVEL 4 [PDF]
International Journal of Number Theory, 2014 Let [Formula: see text] be the space of weakly holomorphic modular forms of weight k and level 4 that are holomorphic away from the cusp at ∞. We define a canonical basis for this space and show that for almost all of the basis elements, the majority of their zeros in a fundamental domain for Γ0(4) lie on the lower boundary of the fundamental domain ...
Haddock, Andrew, Jenkins, Paul
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On the Zeros and Coefficients of Certain Weakly Holomorphic Modular Forms [PDF]
Pure and Applied Mathematics Quarterly, 2008 A \textit{weakly holomorphic modular form} (say, \(f\)) of weight \(k\in 2\mathbb{Z}\) for the full modular group \(\mathrm{PSL}_{2}(\mathbb{Z})\) is defined the same way as holomorphic modular form, only \(f\) is allowed to have a finite number of negative powers in its \(q\)-expansion. Write \(k=12\ell+k'\) with uniquely determined \(\ell\in\mathbb{Z}
Duke, W., Jenkins, Paul
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On coefficients of Poincaré series and single-valued periods of modular forms. [PDF]
Res Math Sci, 2020 We prove that the field generated by the Fourier coefficients of weakly holomorphic Poincaré series of a given level 0() and integral weight ≥2 coincides with the field generated by the single-valued periods of a certain motive attached to 0().
Fonseca TJ.
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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 ...
Bringmann, Kathrin +2 more
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Analogues of the Bol operator for half-integral weight weakly holomorphic modular forms
, 2022 We define an analogue of the Bol operator on spaces of weakly holomorphic modular forms of half-integral weight.
Lee, Min +6 more
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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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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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