Poles of Artin L-functions and the strong Artin conjecture

AR Booker

Poles of Artin L-functions and the strong Artin conjecture

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Abstract

We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture.

Translated title of the contribution	Poles of Artin L-functions and the strong Artin conjecture
Original language	English
Pages (from-to)	1089 - 1098
Number of pages	10
Journal	Annals of Mathematics
Volume	158 (3)
Publication status	Published - Nov 2003

Bibliographical note

Publisher: Johns Hopkins University Press
Other identifier: IDS number 774EX

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title = "Poles of Artin L-functions and the strong Artin conjecture",

abstract = "We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture.",

author = "AR Booker",

note = "Publisher: Johns Hopkins University Press Other identifier: IDS number 774EX",

year = "2003",

month = nov,

language = "English",

volume = "158 (3)",

pages = "1089 -- 1098",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Princeton University Press",

}

TY - JOUR

T1 - Poles of Artin L-functions and the strong Artin conjecture

AU - Booker, AR

N1 - Publisher: Johns Hopkins University Press Other identifier: IDS number 774EX

PY - 2003/11

Y1 - 2003/11

N2 - We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture.

AB - We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture.

M3 - Article (Academic Journal)

VL - 158 (3)

SP - 1089

EP - 1098

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

ER -

Poles of Artin L-functions and the strong Artin conjecture

Abstract

Bibliographical note

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