Results 91 to 100 of about 129 (113)

Two-divisibility of the coefficients of certain weakly holomorphic modular forms [PDF]

Ramanujan Journal, 2012
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 ...
Darrin Doud, Paul Jenkins, Jenkins Paul   +2 more
exaly   +3 more sources

ARITHMETIC OF WEAKLY HOLOMORPHIC MODULAR FORMS FOR HECKE GROUPS

JP Journal of Algebra, Number Theory and Applications, 2015
Summary: \textit{W. Duke} and \textit{P. Jenkins} [Pure Appl. Math. Q. 4, No. 4, 1327--1340 (2008; Zbl 1200.11027)] constructed a nice canonical basis for the space of weakly holomorphic modular forms of weight \(k\) for \(\mathrm{SL}_2(\mathbb{Z})\) that are holomorphic away from the cusp at infinity.
Ahn, Jaehyun, Choi, Soyoung
openaire   +1 more source

Zagier duality and integrality of Fourier coefficients for weakly holomorphic modular forms

Journal of Number Theory, 2015
Worked out the isomorphisms for a general sign vector; proved Zagier duality for canonical bases; raise a question on integrality; 24 ...
Yichao Zhang
exaly   +3 more sources

Hecke structures of weakly holomorphic modular forms and their algebraic properties

Journal of Number Theory, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Subong Lim, Dohoon Choi
exaly   +3 more sources

Basis for the space of weakly holomorphic modular forms in higher level cases

Journal of Number Theory, 2013
Let \(p\) be either \(1\) or a prime number. Let \(\Gamma_0(p)^+\) be the group generated by the group \(\Gamma_0(p)\) and the Fricke involution \(W_p\) and \(M_k^!(\Gamma_0(p)^+)\) be the space of weakly holomorphic modular forms (that is, meromorphic with poles only at the cusps) of even integral weight \(k\) with respect to \(\Gamma_0(p)^+\).
Chang Heon Kim, Soyoung Choi
exaly   +3 more sources

A basis for the space of weakly holomorphic Drinfeld modular forms of level T

Journal of Number Theory
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
exaly   +3 more sources

Zeros of weakly holomorphic modular forms of levels 2 and 3 [PDF]

Mathematical Research Letters, 2013
Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $Γ_0(N)$ that are holomorphic at all cusps except possibly at $\infty$. We study a canonical basis for $M_k^\sharp(2)$ and $M_k^\sharp(3)$ and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a ...
Paul Jenkins, Jenkins Paul
exaly   +4 more sources

The zeros of certain weakly holomorphic Drinfeld modular forms

Manuscripta Mathematica, 2014
Duke and Jenkins (Pure Appl Math Q 4(4):1327–1340, 2008) constructed a canonical basis for the space of weakly holomorphic modular forms for $${{\rm SL}_2(\mathbb{Z})}$$ and investigated the zeros of the ...
SoYoung Choi, Bo-Hae Im
openaire   +1 more source

Three-divisibility of Fourier coefficients of weakly holomorphic modular forms

Ramanujan Journal, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +3 more sources

A basis for the space of weakly holomorphic Drinfeld modular forms for GL2(A)

Journal of Number Theory, 2022
Abstract We construct a canonical basis for the space of weakly holomorphic Drinfeld modular forms. And we find that the basis elements satisfy a generating function and the duality among coefficients of the basis elements. Moreover we obtain the congruence properties of t-expansion coefficients of these functions under some conditions.
openaire   +1 more source