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Doubling Constructions and Tensor Product L-Functions: the linear case

Yuanqing Cai Weizmann Institute of Science Solomon Friedberg Boston College David Ginzburg Tel Aviv University Eyal Kaplan Bar Ilan University

Number Theory Representation Theory mathscidoc:2105.24001

Invent. Math., 217, (3), 985–1068, 2019.9
We present an integral representation for the tensor product L-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.
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@inproceedings{yuanqing2019doubling,
  title={Doubling Constructions and Tensor Product L-Functions: the linear case},
  author={Yuanqing Cai, Solomon Friedberg, David Ginzburg, and Eyal Kaplan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210512132431664896822},
  booktitle={Invent. Math.},
  volume={217},
  number={3},
  pages={985–1068},
  year={2019},
}
Yuanqing Cai, Solomon Friedberg, David Ginzburg, and Eyal Kaplan. Doubling Constructions and Tensor Product L-Functions: the linear case. 2019. Vol. 217. In Invent. Math.. pp.985–1068. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210512132431664896822.
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