Zagier duality and integrality for Fourier coefficients for weakly holomorphic modular forms

2013/08/05 by Yichao Zhang, Zhang, Yichao
Mathematics · #11F27 #11F30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1308.1037

openalex publication_date 2013/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we generalize the isomorphisms to the case when the discriminant form is not necessarily induced from real quadratic fields. In particular, this general setting includes all the subspaces with epsilon-conditions, only two spacial cases of which were treated before. With this established, we shall prove the Zagier duality for canonical bases. Finally, we raise a question on the integrality of the Fourier coefficients of these bases elements, or equivalently we concern the existence of a Miller-like basis for vector valued modular forms.

Citations

• Arithmetic properties of coefficients of half-integral weight Maass–Poincaré series
• An Isomorphism between Scalar-Valued Modular Forms and Modular Forms for Weil Representations

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