Results 1 to 10 of about 6,121 (156)
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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Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms [PDF]
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 values of weakly holomorphic modular functions at divisors of meromorphic modular forms [PDF]
Journal of Number Theory, 2021 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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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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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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A Basis for the space of weakly holomorphic Drinfeld modular forms of level $T$ [PDF]
Journal of Number Theory, 2023 In this article, we explicitly construct a canonical basis for the space of certain weakly holomorphic Drinfeld modular forms for $Γ_0(T)$ (resp., for $Γ_0^+(T)$) and compute the generating function satisfied by the basis elements. We also give an explicit expression for the action of the $Θ$-operator, which depends on the divisor of meromorphic ...
Tarun Dalal
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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 $\Gamma_0 (N)$.
Stephanie Treneer
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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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Weakly holomorphic modular forms for some moonshine groups [PDF]
Archiv der Mathematik, 2014 In an article in the Pure and Applied Mathematics Quarterly in 2008, Duke and Jenkins investigated a certain natural basis of the space of weakly holomorphic modular forms for the full modular group $SL_2({\bf Z})$. We show here that their results can be generalized to certain moonshine groups, also allowing characters that are real on the underlying ...
Martina Lahr, Rainer Schulze‐Pillot
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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 a number field L L . Write q = e 2 π i z q = e^{2 \pi i z} , and suppose that f ( z ) = ∑
Spencer Dembner, Vanshika Jain
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