Results 11 to 20 of about 156 (139)
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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Open Mathematics, 2019 After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
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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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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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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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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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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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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 weight k
Paul Jenkins, Kyle Pratt
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