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arXiv · 2306.07026

On gamma factors of Rankin--Selberg integrals for $\mathrm{U}_{2\ell} \times \mathrm{Res}_{E / F} \mathrm{GL}_n$

Kazuki Morimoto
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Abstract

In this paper, we prove the fundamental properties of gamma factors defined by Rankin-Selberg integrals of Shimura type for pairs of generic representations $(\pi, \tau)$ 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 $(\pi, \tau_1 \times \tau_2)$ 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.

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Kazuki Morimoto. 2023-06-12. On gamma factors of Rankin--Selberg integrals for $\mathrm{U}_{2\ell} \times \mathrm{Res}_{E / F} \mathrm{GL}_n$. https://arxiv.org/abs/2306.07026

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