Nonvanishing of the central critical value of the third symmetric power L-functions

David Ginzburg; Dihua Jiang; Stephen Rallis

doi:10.1515/form.2001.001

Nonvanishing of the central critical value of the third symmetric power L-functions

David Ginzburg^*, Dihua Jiang, Stephen Rallis

^*Corresponding author for this work

School of Mathematical Sciences

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

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Abstract

In this paper we characterize the nonvanishing of the central critical value of the third symmetric power L-functions of irreducible cuspidal automorphic representations π of GL₂(double-struck A sign) in terms of the occurrence of π in the spectral decomposition of the tensor product of two automorphic theta representations on the cubic cover of GL₂(double-struck A sign), which was constructed by Kazhdan and Patterson in [KP].

Original language	English
Pages (from-to)	109-132
Number of pages	24
Journal	Forum Mathematicum
Volume	13
Issue number	1
DOIs	https://doi.org/10.1515/form.2001.001
State	Published - 2001

Funding

Funders	Funder number
National Science Foundation	DMS-9896257
National Science Foundation

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10.1515/form.2001.001

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abstract = "In this paper we characterize the nonvanishing of the central critical value of the third symmetric power L-functions of irreducible cuspidal automorphic representations π of GL2(double-struck A sign) in terms of the occurrence of π in the spectral decomposition of the tensor product of two automorphic theta representations on the cubic cover of GL2(double-struck A sign), which was constructed by Kazhdan and Patterson in [KP].",

author = "David Ginzburg and Dihua Jiang and Stephen Rallis",

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AU - Rallis, Stephen

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N2 - In this paper we characterize the nonvanishing of the central critical value of the third symmetric power L-functions of irreducible cuspidal automorphic representations π of GL2(double-struck A sign) in terms of the occurrence of π in the spectral decomposition of the tensor product of two automorphic theta representations on the cubic cover of GL2(double-struck A sign), which was constructed by Kazhdan and Patterson in [KP].

AB - In this paper we characterize the nonvanishing of the central critical value of the third symmetric power L-functions of irreducible cuspidal automorphic representations π of GL2(double-struck A sign) in terms of the occurrence of π in the spectral decomposition of the tensor product of two automorphic theta representations on the cubic cover of GL2(double-struck A sign), which was constructed by Kazhdan and Patterson in [KP].

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Nonvanishing of the central critical value of the third symmetric power L-functions

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