Nonsolvable number fields ramified only at 3 and 5

@article{Dembl2009NonsolvableNF,
  title={Nonsolvable number fields ramified only at 3 and 5},
  author={Lassina Demb{\'e}l{\'e} and Matthew Greenberg and John Voight},
  journal={Compositio Mathematica},
  year={2009},
  volume={147},
  pages={716 - 734}
}
Abstract 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. 
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