Results 11 to 20 of about 6,496 (142)

On the zeros of weakly holomorphic modular forms [PDF]

Archiv Der Mathematik, 2014
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.
Gun, Sanoli, Saha, Biswajyoti
core   +5 more sources

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 ...
Paul Jenkins
exaly   +3 more sources

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
semanticscholar   +4 more sources

$p$-adic properties of coefficients of weakly holomorphic modular forms [PDF]

International Mathematics Research Notices, 2009
We examine the Fourier coefficients of modular forms in a canonical basis for the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coefficients are often highly divisible by the primes 2, 3, and 5.Comment: 16
Doud, Darrin, Jenkins, Paul
core   +3 more sources

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}
W. Duke, P. Jenkins
semanticscholar   +4 more sources

Algebraic de Rham theory for weakly holomorphic modular forms of level one [PDF]

Algebra & Number Theory, 2017
We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients.
F. Brown, R. Hain
semanticscholar   +6 more sources

Half-integral weight p-adic coupling of weakly holomorphic and holomorphic modular forms [PDF]

Research in Number Theory, 2015
In this paper, we consider p-adic limits of β−ng|Up2n$\beta ^{-n}g|U_{p^{2}}^{n}$ for half-integral weight weakly holomorphic Hecke eigenforms g with eigenvalue λp=β+β′ under Tp2$T\phantom {\dot {i}\!}_{p^{2}}$ and prove that these equal classical Hecke ...
K. Bringmann, P. Guerzhoy, B. Kane
semanticscholar   +6 more sources

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
semanticscholar   +2 more sources

HECKE OPERATORS FOR WEAKLY HOLOMORPHIC MODULAR FORMS AND SUPERSINGULAR CONGRUENCES [PDF]

Proceedings of the American Mathematical Society, 2008
We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.
P. Guerzhoy
semanticscholar   +5 more sources

Hecke grids and congruences for weakly holomorphic modular forms

, 2013
Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain residue ...
Ahlgren, Scott, Andersen, Nickolas
core   +2 more sources