Zagier duality for harmonic weak Maass forms of integral weight

2010/11/19 by Bumkyu Cho, YoungJu Choie · 1 citation
Mathematics · #Advanced Mathematical Identities #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.1090/s0002-9939-2010-10751-7

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.

Citations

• The f(q) mock theta function conjecture and partition ranks
• Dyson’s ranks and Maass forms

Cited by

• On harmonic weak Maass forms of half integral weight
• Structures for pairs of mock modular forms with the Zagier duality

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• Zagier duality for harmonic weak Maass forms of integral weight
• On harmonic weak Maass forms of half integral weight
• Structures for pairs of mock modular forms with the Zagier duality
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