Results 21 to 30 of about 156 (139)
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.
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Congruences involving the $$U_{\ell }$$ operator for weakly holomorphic modular forms [PDF]
The Ramanujan Journal, 2019 Let $λ$ be an integer, and $f(z)=\sum_{n\gg-\infty} a(n)q^n$ be a weakly holomorphic modular form of weight $λ+\frac 12$ on $Γ_0(4)$ with integral coefficients. Let $\ell\geq 5$ be a prime. Assume that the constant term $a(0)$ is not zero modulo $\ell$.
Choi, Dohoon, Lim, Subong
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Modular bootstrap for D4-D2-D0 indices on compact Calabi-Yau threefolds
, 2022 We investigate the modularity constraints on the generating series $h_r(\tau)$ of BPS indices counting D4-D2-D0 bound states with fixed D4-brane charge $r$ in type IIA string theory compactified on complete Intersection Calabi-Yau threefolds with $b_2 ...
Pioline, Boris +5 more
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Rank generating functions as weakly holomorphic modular forms [PDF]
Acta Arithmetica, 2008 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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Petersson inner products of weight-one modular forms
, 2019 In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients.
Viazovska, Maryna
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Zeros of certain weakly holomorphic modular forms for the Fricke group ${\varGamma }_0^+(3)$
Acta Arithmetica, 2021 19 ...
Hanamoto, Seiichi, Kuga, Seiji
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Duality and differential operators for harmonic Maass forms [PDF]
, 2013 Due to the graded ring nature of classical modular forms, there are many interesting relations between the coefficients of different modular forms. We discuss additional relations arising from Duality, Borcherds products, theta lifts.
Bringmann, K, Kane, B, Rhoades, RC
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A Note on Fourier Eigenfunctions in Four Dimensions
, 2022 In this note, we exhibit a weakly holomorphic modular form for use in constructing a Fourier eigenfunction in four dimensions. Such auxiliary functions may be of use to the D4 checkerboard lattice and the four dimensional sphere packing problem.Comment ...
Lautzenheiser, Daniel +1 more
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Weakly holomorphic modular forms in prime power levels of genus zero
Integers, 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 coefficients of the basis elements in $M_0^\sharp(N)$ are divisible by high powers of the prime ...
Paul Jenkins, DJ Thornton
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Eichler-Shimura theory for mock modular forms
, 2013 We use mock modular forms to compute generating functions for the critical values of modular L-functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the “extra relation ” that is satisfied by even periods of weakly ...
Kent, Zachary +7 more
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