On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras

Beneish, Lea; Mertens, Michael H.

doi:10.1007/s00209-020-02499-4

Cited by 4 publications

(2 citation statements)

References 48 publications

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“…(2) Niebur-Poincaré seris is the Maass-Poincaré series of weight 0. Proposition 3.1 of [4] gives the proof of the same result with Corollary 1.4 for Maass-Poincaré series on Γ 0 (N ) of any nonpositive weights to establish dimension formulas for certain vertex operator algebras. Our proof can also be extended to Maass-Poincaré series.…”

Section: Introductionmentioning

confidence: 73%

Hecke System of Harmonic Maass Functions and Applications to Modular Curves of Higher Genera

Jeon¹,

Kang²,

Kim³

2020

Preprint

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In Monstrous moonshine, genus 0 property and the notion of replicability are strongly connected. With regards to recent developments of moonshine, we investigate a higher genus generalization of replicability for a general automorphic form. Specifically, we extend the definitions of replicates and a Hecke operator to harmonic Maass functions on modular curves of higher genera to obtain number theoretic generalizations of important results in Monstrous moonshine. Furthermore, we show the utility of the extended notions in yielding uniform proofs for numerous arithmetic properties of Fourier coefficients of modular functions of arbitrary level, which have been proved only for special cases of curves of genus zero or small prime levels.

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Section: Introductionmentioning

confidence: 73%

Hecke System of Harmonic Maass Functions and Applications to Modular Curves of Higher Genera

Jeon¹,

Kang²,

Kim³

2020

Preprint

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“…These preimages Z E can be computed very efficiently and are also of theoretical interest. In [AGOR15], they were used to obtain a criterion for the vanishing of critical L-derivatives of quadratic twists of E. Another application in the context of vertex operator algebras can be found in [BM21].…”

Section: Introductionmentioning

confidence: 99%

Modular Forms

Alfes-Neumann

2021

Modular Forms

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We construct harmonic weak Maass forms that map to cusp forms of weight k ≥ 2 with rational coefficients under the ξ-operator. This generalizes work of the first author, Griffin, Ono, and Rolen, who constructed distinguished preimages under this differential operator of weight 2 newforms associated to rational elliptic curves using the classical Weierstrass theory of elliptic functions. We extend this theory and construct a vector-valued Jacobi-Weierstrass ζ-function which is a generalization of the classical Weierstrass ζ-function.

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The Hecke system of harmonic Maass functions and applications to modular curves of higher genera

2023

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On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras

Cited by 4 publications

References 48 publications

Hecke System of Harmonic Maass Functions and Applications to Modular Curves of Higher Genera

Hecke System of Harmonic Maass Functions and Applications to Modular Curves of Higher Genera

Modular Forms

The Hecke system of harmonic Maass functions and applications to modular curves of higher genera

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