关于 SO5 × GL2 的兰金-塞尔伯格 L 因子

Pub Date : 2023-11-29 DOI:10.1007/s11856-023-2580-y

Yao Cheng

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引用次数: 0

摘要

假设π和τ分别是非拱顶局部域上 SO5 和 GL2 的不可还原光滑通称表示。我们证明，由 Rankin-Selberg 积分定义的附加于 π×π 的 L 因子和 ε 因子与相关的 Weil-Deligne 表示重合。通过解释 SO5 × GL2 的兰金-塞尔伯格积分与 GSp4× GL2 的诺沃德沃斯基局部积分之间的关系，可以得到证明。

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On the Rankin–Selberg L-factors for SO5 × GL2

Let π and τ be irreducible smooth generic representations of SO₅ and GL₂ respectively over a non-archimedean local field. We show that the L- and ε-factors attached to π×π defined by the Rankin–Selberg integrals and the associated Weil–Deligne representation coincide. The proof is obtained by explicating the relation between the Rankin–Selberg integrals for SO₅ × GL₂ and Novodvorsky’s local integrals for GSp₄× GL₂.

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