Results 1 to 10 of about 3,783 (150)
On cycle integrals of weakly holomorphic modular forms [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2014 In 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.
Bringmann, Kathrin +2 more
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Hecke grids and congruences for weakly holomorphic modular forms [PDF]
, 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
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$p$-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
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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
doaj +3 more sources
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
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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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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 $\Gamma_0(N)$ 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 ...
Garthwaite, Sharon Anne, Jenkins, Paul
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Weakly holomorphic modular forms in prime power levels of genus zero [PDF]
, 2017 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 ...
Da Silva, Caroline M. +3 more
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Two-divisibility of the coefficients of certain weakly holomorphic modular forms [PDF]
The Ramanujan Journal, 2011 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 ...
A. El-Guindy +18 more
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Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2013 We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications.
Ahlgren, Scott, Kim, Byungchan
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