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arXiv · 2606.27212

A direct proof of Mono-Rolen-Stumpenhusen and new constructions via the Maass raising operators

Kathrin Bringmann·Ben Kane
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Abstract

In this paper, we give a direct conceptual proof of the main result of Mono, Rolen, and Stumpenhusen, using differential operators. More precisely, we realize their functions $\omega_{k+1,D}$ as images of the quadratic form Poincar\'e series $f_{k,D}$ under the Maass raising operator. This perspective gives a natural explanation for the modularity and Laplace eigenvalue prop erties of $\omega_{k+1,D}$. We further extend these results by investigating the images of more general local Maass forms under the Maass raising and lowering operators.

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Kathrin Bringmann, Ben Kane. 2026-06-25. A direct proof of Mono-Rolen-Stumpenhusen and new constructions via the Maass raising operators. https://arxiv.org/abs/2606.27212

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