Doubling constructions and tensor product L-functions: the linear case
Doubling constructions and tensor product L-functions: the linear case
复制标题
DOI：
10.1007/s00222-019-00883-4
复制
发表时间：
2017-10
影响因子：
3.1
通讯作者：
Yuanqing Cai;S. Friedberg;D. Ginzburg;Eyal Kaplan
中科院分区：
文献类型：
--
作者：
Yuanqing Cai;S. Friedberg;D. Ginzburg;Eyal Kaplan
给出了一对自同构尖球面表示的张量积L-函数的积分表示，其中一个是经典群，另一个是一般线性群。我们的构造在所有经典群上是一致的，并且适用于所有的尖锥表示；它不需要通用性。构造的主要新想法是使用广义Speh表示作为Eisenstein级数的诱导数据，并引入一个新的(全局和局部)模型，该模型推广了Whittaker模型。在这里，我们考虑线性群，但我们的构造也扩展到任意次亚可积覆盖；这将是即将到来的工作的主题。
We present an integral representation for the tensor productL-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and local) model, which generalizes the Whittaker model. Here we consider linear groups, but our construction also extends to arbitrary degree metaplectic coverings; this will be the topic of an upcoming work.