Arithmetic properties for the minus space of weakly holomorphic modular forms
Abstract Let M k ! ( p ) be the space of weakly holomorphic modular forms of weight k on Γ 0 ( p ) , and let M k ! − ( p ) be the minus space which is the subspace of M k ! ( p ) consisting of all eigenforms of the Fricke involution W p with eigenvalue −1.
Soyoung Choi+2 more
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Weakly holomorphic modular forms in prime power levels of genus zero
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
core +6 more sources
Special $L$-values and periods of weakly holomorphic modular forms [PDF]
In this paper, we explore a method for associating L-series to weakly holomorphic modular forms and then proceed to study their L-values. As our main application, we prove a very curious limiting theorem which relates three “periods” of a mock modular ...
Kathrin Bringmann+2 more
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Zeros of certain weakly holomorphic modular forms for the Fricke group $Γ_0^+(3)$
Comment: 19 ...
Seiichi Hanamoto, Seiji Kuga
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On the Zeros and Coefficients of Certain Weakly Holomorphic Modular Forms [PDF]
For this paper we assume familiarity with the basics of the theory of modular forms as may be found, for instance, in Serre’s classic introduction [12]. A weakly holomorphic modular form of weight k ∈ 2Z for Γ = PSL2(Z) is a holomorphic function f on the
William Duke, Paul A. Jenkins
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Zagier duality and integrality of Fourier coefficients for weakly holomorphic modular forms [PDF]
Worked out the isomorphisms for a general sign vector; proved Zagier duality for canonical bases; raise a question on integrality; 24 ...
Yichao Zhang
openalex +4 more sources
Two-divisibility of the coefficients of certain weakly holomorphic modular forms [PDF]
We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly ...
Paul Jenkins, John Lopez, Darrin Doud
openaire +4 more sources
On the zeros of weakly holomorphic modular forms [PDF]
In this article, we study the nature of zeros of weakly holomorphic modular forms. In particular, we prove results about transcendental zeros of modular forms of higher levels and for certain Fricke groups which extend a work of Kohnen. Furthermore, we investigate the algebraic independence of values of weakly holomorphic modular forms.
Biswajyoti Saha, Sanoli Gun
semanticscholar +6 more sources
Analogues of the Bol operator for half-integral weight weakly holomorphic modular forms [PDF]
We define an analogue of the Bol operator on spaces of weakly holomorphic modular forms of half-integral weight. We establish its main properties and relation with other objects.
Nikolaos Diamantis, Min Lee, Larry Rolen
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Rank generating functions as weakly holomorphic modular forms [PDF]
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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