Let π be an irreducible admissible (complex) representation of $GL(2)$ over a non‐Archimedean characteristic zero local field with odd residual characteristic. In this paper, we prove the equality between the local symmetric square L‐function associated to π arising from integral representations and the corresponding Artin L‐function for its Langlands parameter through the local Langlands correspondence. With this in hand, we show the stability of local symmetric γ‐factors attached to π under highly ramified twists.

中文翻译：

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GL（2）上局部对称平方因子的RANKIN-SELBERG积分

令π为的不可约的可容许（复杂）表示 $G\mathrm{大号}（2）$在具有奇数残留特征的非阿基米德特征零局部场上。在本文中，我们通过局部Langlands对应关系证明了与积分表示相关的与π相关的局部对称平方L函数与对应于其Langlands参数的Artin L函数之间的相等性。有了这个，我们展示了在高度分叉的扭曲下附加到π的局部对称γ因子的稳定性。