A Shintani lift for rigid cocycles
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911845955141632 |
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| author | Negrini, Isabella |
| author_facet | Negrini, Isabella |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12936 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Shintani lift for rigid cocycles Negrini, Isabella Number Theory 11 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. |
| title | A Shintani lift for rigid cocycles |
| topic | Number Theory 11 |
| url | https://arxiv.org/abs/2404.12936 |