Results 11 to 20 of about 3,783 (150)
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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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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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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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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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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Zeros of weakly holomorphic modular forms of level 4 [PDF]
International Journal of Number Theory, 2013 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 ...
A. Glen Haddock, Paul M. Jenkins
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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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Rank generating functions as weakly holomorphic modular forms [PDF]
Acta Arithmetica, 2008 We study infinite families of generating functions involving the rank of the ordinary partition function, which include as special cases many of the generating functions introduced by Atkin and Swinnerton-Dyer in the 1950s. We prove that each of these generating functions is a weakly holomorphic modular form of weight 1/2 on some congruence subgroup Γ1(
Scott Ahlgren, Stephanie Treneer
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Classification of congruences for mock theta functions and weakly\n holomorphic modular forms [PDF]
The Quarterly Journal of Mathematics, 2013 Let $f(q)$ denote Ramanujan's mock theta function \[f(q) = \sum_{n=0}^{\infty} a(n) q^{n} := 1+\sum_{n=1}^{\infty} \frac{q^{n^{2}}}{(1+q)^{2}(1+q^{2})^{2}\cdots(1+q^{n})^{2}}.\] It is known that there are many linear congruences for the coefficients of $f(q)$ and other mock theta functions. We prove that if the linear congruence $a(mn+t) \equiv 0 \pmod{
Nickolas Andersen
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