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arXiv · 2606.18110

Recursions for Mock Theta Functions

Matthew Ortiz·Martin Raum·Olav K. Richter
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Abstract

We establish weighted recursions for the coefficients of Ramanujan's third order mock theta functions $f$ and $\omega$. Specifically, we apply a holomorphic projection operator to vector-valued Rankin-Cohen brackets of completed mock theta series and their shadows. By employing a vector-valued framework, we exploit the vanishing of certain spaces of vector-valued cusp forms. Our proof is AI-assisted and prioritizes accessibility, allowing for straightforward customization and replication within the broader research community.

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Matthew Ortiz, Martin Raum, Olav K. Richter. 2026-06-16. Recursions for Mock Theta Functions. https://arxiv.org/abs/2606.18110

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