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arXiv · 2503.11817

An Improved Lower Bound on the Image of the 2-adic Character Map for the Heisenberg Algebra via Modular Linear Differential Equations

Daniel Barake·Cameron Franc
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Abstract

We describe families of MLDEs whose solutions are modular forms of level one that converge, $2$-adically, to a Hauptmodul on $\Gamma_0(2)$ by using a theorem of Serre. Then, we apply this to show that the image of the character map on the $2$-adic Heisenberg VOA $S_{1}$ contains the space of $2$-adic overconvergent modular forms $M_{2}^{\dagger}(1/2)$ of weight zero.

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Daniel Barake, Cameron Franc. 2025-03-14. An Improved Lower Bound on the Image of the 2-adic Character Map for the Heisenberg Algebra via Modular Linear Differential Equations. https://arxiv.org/abs/2503.11817

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