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Nonsolvable number fields ramified only at 3 and 5

Published online by Cambridge University Press:  15 February 2011

Lassina Dembélé
Affiliation:
Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (email: [email protected])
Matthew Greenberg
Affiliation:
University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4 (email: [email protected])
John Voight
Affiliation:
Department of Mathematics and Statistics, University of Vermont, 16 Colchester Ave, Burlington, VT 05401, USA (email: [email protected])
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Abstract

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For p=3 and p=5, we exhibit a finite nonsolvable extension of ℚ which is ramified only at p, proving in the affirmative a conjecture of Gross. Our construction involves explicit computations with Hilbert modular forms.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2011

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