# 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.

## 9 Citations

### NONSOLVABLE POLYNOMIALS WITH FIELD DISCRIMINANT 5 A

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- 2011

We present the first explicitly known polynomials in Z(x) with nonsolvable Galois group and field discriminant of the form ±p A for p 7 a prime. Our main polyno- mial has degree 25, Galois group of…

### Nonsolvable Polynomials with Field Discriminant 5<sup>a</sup>

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We present the first explicitly known polynomials in Z[x] with nonsolvable Galois group and field discriminant of the form ±pA for p ≤ 7 a prime. Our main polynomial has degree 25, Galois group of…

### Explicit Methods for Hilbert Modular Forms

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- 2013

The study of modular forms remains a dominant theme in modern number theory, a consequence of their intrinsic appeal as well as their applications to a wide variety of mathematical problems. This…

### Hecke stability and weight $$1$$1 modular forms

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- 2014

The Galois representations associated to weight 1 eigenforms over $$\bar{\mathbb {F}}_{p}$$F¯p are remarkable in that they are unramified at $$p$$p, but the effective computation of these modular…

### Lattice Methods for Algebraic Modular Forms on Classical Groups

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- 2014

We use Kneser’s neighbor method and isometry testing for lattices due to Plesken and Souveigner to compute systems of Hecke eigenvalues associated to definite forms of classical reductive algebraic…

### N T ] 2 3 M ay 2 01 0 A non-solvable extension of Q unramified outside 7

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- 2010

We consider a mod 7 Galois representation attached to a genus 2 Siegel cuspforms of level 1 and weight 28 and using some of its Fourier coefficients and eigenvalues computed by N. Skoruppa and the…

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