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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.12936 |
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Table of Contents:
- We construct a Shintani lift for rigid analytic cocycles of higher weight, attaching modular forms of half-integral weight to such cocycles. The expression for the Fourier coefficients of the modular form $\mathcal{RS}(J)$ attached to a cocycle $J$ is given in terms of the residues of $J$, and shares a striking similarity with the expression for the coefficients of the classical Shintani lift $\mathcal{S}(f)$ of an integral weight modular form $f$. This work aligns with the ideas of the nascent $p$-adic Kudla program and strengthens the analogy between rigid cocycles and modular forms.