关于 SO5 × GL2 的兰金-塞尔伯格 L 因子

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics 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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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.