Displaying similar documents to “Constructing modular forms from harmonic Maass Jacobi forms”

Cohen-Kuznetsov liftings of quasimodular forms

Min Ho Lee (2015)

Acta Arithmetica

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Jacobi-like forms for a discrete subgroup Γ of SL(2,ℝ) are formal power series which generalize Jacobi forms, and they correspond to certain sequences of modular forms for Γ. Given a modular form f, a Jacobi-like form can be constructed by using constant multiples of derivatives of f as coefficients, which is known as the Cohen-Kuznetsov lifting of f. We extend Cohen-Kuznetsov liftings to quasimodular forms by determining an explicit formula for a Jacobi-like form associated to a quasimodular...

Asymptotic formulas for the coefficients of certain automorphic functions

Jaban Meher, Karam Deo Shankhadhar (2015)

Acta Arithmetica

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We derive asymptotic formulas for the coefficients of certain classes of weakly holomorphic Jacobi forms and weakly holomorphic modular forms (not necessarily of integral weight) without using the circle method. Then two applications of these formulas are given. Namely, we estimate the growth of the Fourier coefficients of two important weak Jacobi forms of index 1 and non-positive weights and obtain an asymptotic formula for the Fourier coefficients of the modular functions θ k / η l for all...

Linear relations between modular forms for Г 0 + (p)

SoYoung Choi, Chang Heon Kim (2015)

Open Mathematics

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We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.

Shimura lifting on weak Maass forms

Youngju Choie, Subong Lim (2016)

Acta Arithmetica

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There is a Shimura lifting which sends cusp forms of a half-integral weight to holomorphic modular forms of an even integral weight. Niwa and Cipra studied this lifting using the theta series attached to an indefinite quadratic form; later, Borcherds and Bruinier extended this lifting to weakly holomorphic modular forms and harmonic weak Maass forms of weight 1/2, respectively. We apply Niwa's theta kernel to weak Maass forms by using a regularized integral. We show that the lifted function...