论文标题
$ gl \ mathrm {（2）} $的本地对称平方因子的Rankin-Selberg积分
Rankin-Selberg integrals for local symmetric square factors on $GL\mathrm{(2)}$
论文作者
论文摘要
令$π$为非固定特征零本地场上的$ gl（2）$的不可约（复杂）表示，具有奇数残留特征。在本文中，我们证明了与整体表示相关的本地对称平方$ l $ l $ unction与$π$相关的函数与通过本地Langlands通信的Langlands参数的相应Artin $ l $ function引起的。借助此功能，我们显示了在高度分支的曲折下附加到$π$的本地对称$γ$ factor的稳定性。
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.
