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Inventiones mathematicae

, Volume 217, Issue 3, pp 985–1068 | Cite as

Doubling constructions and tensor product L-functions: the linear case

  • Yuanqing Cai
  • Solomon Friedberg
  • David Ginzburg
  • Eyal KaplanEmail author
Article
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Abstract

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.

Mathematics Subject Classification

Primary 11F70 Secondary 11F55 11F66 22E50 22E55 

Notes

Acknowledgements

Part of this work was done while the fourth named author was a Zassenhaus Assistant Professor at The Ohio State University, under the supervision of Jim Cogdell. Eyal wishes to express his gratitude to Jim for his kind encouragement and support. We thank the referee for a very careful reading of the manuscript and for many helpful suggestions. Eyal dedicates his part of the work to his beloved Sophie Kaplan who passed away unexpectedly a few weeks before the submission of the first version of this work.

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Authors and Affiliations

  • Yuanqing Cai
    • 1
    • 2
  • Solomon Friedberg
    • 1
  • David Ginzburg
    • 3
  • Eyal Kaplan
    • 4
    Email author
  1. 1.Department of MathematicsBoston CollegeChestnut HillUSA
  2. 2.Department of MathematicsWeizmann Institute of ScienceRehovotIsrael
  3. 3.School of Mathematical SciencesTel Aviv UniversityRamat Aviv, Tel AvivIsrael
  4. 4.Department of MathematicsBar Ilan UniversityRamat GanIsrael

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