Abstract In this article, we revisit Rankin–Selberg integrals established by Jacquet, Piatetski-Shapiro and Shalika. We prove the equality of Rankin–Selberg local factors defined with Schwartz–Bruhat functions and the factors attached to good sections, introduced by Piatetski-Shapiro and Rallis. Moreover, we propose a notion of exceptional poles in the framework of good sections. For cases of Rankin–Selberg, Asai and exterior square L-functions, the exceptional poles are consistent with well-known exceptional poles which characterize certain distinguished representations.

中文翻译：

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Rankin–Selberg L-functions 通过良好的部分

摘要 在本文中，我们重新审视了 Jacquet、Piatetski-Shapiro 和 Shalika 建立的 Rankin-Selberg 积分。我们证明了由 Schwartz-Bruhat 函数定义的 Rankin-Selberg 局部因子和由 Piatetski-Shapiro 和 Rallis 引入的附加到良好部分的因子的相等性。此外，我们在良好截面的框架中提出了异常极点的概念。对于 Rankin-Selberg、Asai 和外部平方 L 函数的情况，异常极点与表征某些特殊表示的众所周知的异常极点一致。