Duke Mathematical Journal

On icosahedral Artin representations

Kevin Buzzard, Mark Dickinson, Nick Shepherd-Barron, and Richard Taylor

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Abstract

If ρ : Gal(ℚac/ℚ))→GL2(ℂ) is a continuous odd irreducible representation wit nonsolvable image, then under certain local hypotheses we prove that ρ is the representation associated to a weight 1 modular form and hence that the L-function of ρ has an analytic continuation to the entire complex plane.

Article information

Source
Duke Math. J., Volume 109, Number 2 (2001), 283-318.

Dates
First available in Project Euclid: 5 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1091737273

Digital Object Identifier
doi:10.1215/S0012-7094-01-10922-8

Mathematical Reviews number (MathSciNet)
MR1845181

Zentralblatt MATH identifier
1015.11021

Subjects
Primary: 11F80: Galois representations
Secondary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50] 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35] 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]

Citation

Buzzard, Kevin; Dickinson, Mark; Shepherd-Barron, Nick; Taylor, Richard. On icosahedral Artin representations. Duke Math. J. 109 (2001), no. 2, 283--318. doi:10.1215/S0012-7094-01-10922-8. https://projecteuclid.org/euclid.dmj/1091737273


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See also

  • See also: Richard Taylor. On icosahedral Artin representations. II. Amer. J. Math. Vol. 125, No. 3 (2003), pp. 549-566.