The generalized doubling method: local theory

Yuanqing Cai, Solomon Friedberg, Eyal Kaplan

Research output: Contribution to journalArticlepeer-review

Abstract

A fundamental difficulty in the study of automorphic representations, representations of p-adic groups and the Langlands program is to handle the non-generic case. In a recent collaboration with David Ginzburg, we presented a new integral representation for the tensor product L-functions of G×GLk where G is a classical group, that applies to all cuspidal automorphic representations, generic or otherwise. In this work we develop the local theory of these integrals, define the local γ-factors and provide a complete description of their properties. We can then define L- and ϵ-factors at all places, and as a consequence obtain the global completed L-function and its functional equation.

Original languageEnglish
Pages (from-to)1233-1333
Number of pages101
JournalGeometric and Functional Analysis
Volume32
Issue number6
DOIs
StatePublished - Dec 2022

Bibliographical note

Funding Information:
Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, Rehovot 76100, Israel; e-mail: dmitry.gourevitch@weizmann.ac.il. Dmitry Gourevitch was supported by the ERC, StG grant number 637912 and by the Israel Science Foundation, grant number 249/17.

Funding Information:
This research was supported by the ERC, StG grant number 637912 (Cai), by the JSPS KAKENHI grant number 19F19019 (Cai), by MEXT Leading Initiative for Excellent Young Researchers Grant Number JPMXS0320200394 (Cai), by the BSF, grant number 2012019 (Friedberg), by the NSF, Grant Numbers 1500977, 1801497 and 2100206 (Friedberg), and by the Israel Science Foundation, grant numbers 376/21 and 421/17 (Kaplan)

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

  • Doubling method
  • Eisenstein series
  • Functoriality
  • General spin groups
  • Non-generic automorphic representation
  • Rankin–Selberg L-function
  • Unipotent orbit

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