二重构造与张量积$L$-函数：辛群的覆盖
Doubling Constructions and Tensor Product $L$-Functions: coverings of the symplectic group
摘要：
在这项工作中，我们开发了一个积分表示部分$L$-功能的一对$π\timesτ$的真正的不可约尖形自守表示，$π$的$m$-折叠覆盖的松本的辛群$Sp_{2n}$，和$τ$的一定覆盖群的$GL_k$，与任意的$m$，$n$和$k$。我们的建设是基于最近的扩展蔡，弗里德伯格，金兹伯格和作者，经典的加倍方法的Piatetski-Shapiro和拉利斯，从秩PDMATHAMV扭曲任意秩扭曲。我们证明了一个基本的整体身份的积分和计算的局部积分与unramified数据。可能的应用包括一个分析定义的局部因素的代表性的覆盖群，和一个志村型电梯的代表性从覆盖群一般线性群。
英文摘要：
In this work we develop an integral representation for the partial $L$-function of a pair $π\timesτ$ of genuine irreducible cuspidal automorphic representations, $π$ of the $m$-fold covering of Matsumoto of the symplectic group $Sp_{2n}$, and $τ$ of a certain covering group of $GL_k$, with arbitrary $m$, $n$ and $k$. Our construction is based on the recent extension by Cai, Friedberg, Ginzburg and the author, of the classical doubling method of Piatetski-Shapiro and Rallis, from rank-$1$ twists to arbitrary rank twists. We prove a basic global identity for the integral and compute the local integrals with unramified data. Possible applications include an analytic definition of local factors for representations of covering groups, and a Shimura type lift of representations from covering groups to general linear groups.
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