Zagier duality for harmonic weak Maass forms of integral weight

Cho, Bumkyu; Choie, YoungJu

doi:10.1090/S0002-9939-2010-10751-7

Zagier duality for harmonic weak Maass forms of integral weight
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by Bumkyu Cho and YoungJu Choie PDF

Proc. Amer. Math. Soc. 139 (2011), 787-797 Request permission

Abstract:

We show the existence of “Zagier duality” between vector valued harmonic weak Maass forms and vector valued weakly holomorphic modular forms of integral weight. This duality phenomenon arises naturally in the context of harmonic weak Maass forms as developed in recent works by Bruinier, Funke, Ono, and Rhoades. Concerning the isomorphism between the spaces of scalar and vector valued harmonic weak Maass forms of integral weight, Zagier duality between scalar valued ones is derived.

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