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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.07026 |
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| _version_ | 1866910642668044288 |
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| author | Morimoto, Kazuki |
| author_facet | Morimoto, Kazuki |
| contents | In this paper, we prove the fundamental properties of gamma factors defined by Rankin-Selberg integrals of Shimura type for pairs of generic representations $(π, τ)$ of $\mathrm{U}_{2\ell}(F)$ and $\mathrm{GL}_n(E)$ for a local field $F$ of characteristic zero and a quadratic extension $E$ of $F$. We also prove similar results for pairs of generic representations $(π, τ_1 \times τ_2)$ of $\mathrm{GL}_{2\ell}(F)$ and $\mathrm{GL}_n(F) \times \mathrm{GL}_n(F)$. As a corollary, we prove that the gamma factors arising from Langlands--Shahidi method and our gamma factors coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07026 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On gamma factors of Rankin--Selberg integrals for $\mathrm{U}_{2\ell} \times \mathrm{Res}_{E / F} \mathrm{GL}_n$ Morimoto, Kazuki Number Theory In this paper, we prove the fundamental properties of gamma factors defined by Rankin-Selberg integrals of Shimura type for pairs of generic representations $(π, τ)$ of $\mathrm{U}_{2\ell}(F)$ and $\mathrm{GL}_n(E)$ for a local field $F$ of characteristic zero and a quadratic extension $E$ of $F$. We also prove similar results for pairs of generic representations $(π, τ_1 \times τ_2)$ of $\mathrm{GL}_{2\ell}(F)$ and $\mathrm{GL}_n(F) \times \mathrm{GL}_n(F)$. As a corollary, we prove that the gamma factors arising from Langlands--Shahidi method and our gamma factors coincide. |
| title | On gamma factors of Rankin--Selberg integrals for $\mathrm{U}_{2\ell} \times \mathrm{Res}_{E / F} \mathrm{GL}_n$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2306.07026 |