Results 1 to 10 of about 6,496 (142)
Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms
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 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.
K. Bringmann, P. Guerzhoy, B. Kane
semanticscholar +11 more sources
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
doaj +6 more sources
Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3 [PDF]
Mathematical Research Letters, 2012 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 ...
S. Garthwaite, P. Jenkins
semanticscholar +6 more sources
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 ...
Yingkun Li, Shaul Zemel
semanticscholar +5 more sources
A note on congruences for weakly holomorphic modular forms [PDF]
Proceedings of the American Mathematical Society, 2020 Let $O_L$ be the ring of integers of a number field $L$. Write $q = e^{2 \pi i z}$, and suppose that $$f(z) = \sum_{n \gg - \infty}^{\infty} a_f(n) q^n \in M_{k}^{!}(\operatorname{SL}_2(\mathbb{Z})) \cap O_L[[q]]$$ is a weakly holomorphic modular form of
S. Dembner, Vanshika Jain
semanticscholar +4 more sources
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.
D. Jeon, Soon-Yi Kang, Chang Heon Kim
semanticscholar +5 more sources
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 $\Gamma_0(T)$ (resp., for $\Gamma_0^+(T)$) and compute the generating function satisfied by the basis elements. We also give
Tarun Dalal
semanticscholar +3 more sources
Curves on K3 surfaces in divisibility 2
Forum of Mathematics, Sigma, 2021 We prove a conjecture of Maulik, Pandharipande and Thomas expressing the Gromov–Witten invariants of K3 surfaces for divisibility 2 curve classes in all genera in terms of weakly holomorphic quasi-modular forms of level 2.
Younghan Bae, Tim-Henrik Buelles
doaj +1 more source
4-manifolds and topological modular forms
Journal of High Energy Physics, 2021 We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds.
Sergei Gukov +3 more
doaj +1 more source