Twisted symmetric square L-functions for GL n and invariant trilinear forms

Eyal Kaplan; Shunsuke Yamana

doi:https://doi.org/10.1007/s00209-016-1726-6

Twisted symmetric square L-functions for GL _n and invariant trilinear forms

Eyal Kaplan, Shunsuke Yamana

Research output: Contribution to journal › Article › peer-review

Abstract

Following the works of Bump and Ginzburg and of Takeda, we develop a theory of twisted symmetric square L-functions for GL _n. We characterize their pole in terms of certain trilinear period integrals, determine all irreducible summands of the discrete spectrum of GL _n having nonvanishing trilinear periods, and construct nonzero local invariant trilinear forms on a certain family of induced representations.

Original language	English
Pages (from-to)	739-793
Number of pages	55
Journal	Mathematische Zeitschrift
Volume	285
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-016-1726-6
State	Published - 1 Apr 2017
Externally published	Yes

Keywords

Distinguished representations
Exceptional representations
Rankin–Selberg integral representation
Symmetric square L-functions

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1007/s00209-016-1726-6

Cite this

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abstract = "Following the works of Bump and Ginzburg and of Takeda, we develop a theory of twisted symmetric square L-functions for GL n. We characterize their pole in terms of certain trilinear period integrals, determine all irreducible summands of the discrete spectrum of GL n having nonvanishing trilinear periods, and construct nonzero local invariant trilinear forms on a certain family of induced representations.",

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AB - Following the works of Bump and Ginzburg and of Takeda, we develop a theory of twisted symmetric square L-functions for GL n. We characterize their pole in terms of certain trilinear period integrals, determine all irreducible summands of the discrete spectrum of GL n having nonvanishing trilinear periods, and construct nonzero local invariant trilinear forms on a certain family of induced representations.

KW - Distinguished representations

KW - Exceptional representations

KW - Rankin–Selberg integral representation

KW - Symmetric square L-functions

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