Rank-Crank type PDE's for higher level Appell functions

Sander Zwegers

Displaying similar documents to “Rank-Crank type PDE's for higher level Appell functions”

On the Andrianov-type identity for power series attached to Jacobi forms and its application

Hidenori Katsurada, Hisa-aki Kawamura (2010)

Acta Arithmetica

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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...

Jacobi forms and a certain space of modular forms.

Don Zagier, Nils-Peter Skoruppa (1988)

Inventiones mathematicae

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Periods of modular forms and Jacobi theta functions.

Don Zagier (1991)

Inventiones mathematicae

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A decomposition theorem for Jacobi forms.

Joachim Dulinski (1995)

Mathematische Annalen

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Jacobi forms and certain special values of Dirichlet series associated to modular form.

Takakazu Satoh (1989)

Mathematische Annalen

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Explicit formulas for the Fourier coefficients of Jacobi and elliptic modular forms.

Nils-Peter Skoruppa (1990)

Inventiones mathematicae

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Constructing modular forms from harmonic Maass Jacobi forms

Ran Xiong, Haigang Zhou (2021)

Czechoslovak Mathematical Journal

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We construct a family of modular forms from harmonic Maass Jacobi forms by considering their Taylor expansion and using the method of holomorphic projection. As an application we present a certain type Hurwitz class relations which can be viewed as a generalization of Mertens' result in M. H. Mertens (2016).