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arXiv · 2404.12936

A Shintani lift for rigid cocycles

Isabella Negrini
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Abstract

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.

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Isabella Negrini. 2024-04-19. A Shintani lift for rigid cocycles. https://arxiv.org/abs/2404.12936

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