Number fields with discriminant +-2^a 3^b: Examples from three point covers

1998/10/27 by David P. Roberts, Roberts, David P.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/9810210

arxiv created 1998/10/27 · arxiv updated 2009/12/01

Abstract

In this paper we construct number fields ramified at 2 and 3 only, with various moderate-sized non-solvable Galois groups. We construct these fields by specializing three point covers, some from the literature and some new here. The specialization points come from solutions to a generalized Fermat equation. We conclude with a specific suggestion for further research and two general conjectures.

Related

• Lightly ramified number fields with Galois group S.M₁₂.A
• Mixed degree number field computations
• On number fields with k-free discriminants
• On small discriminants of number fields of degree 8 and 9
• Upper Bounds for the Number of Number Fields with Alternating Galois\n Group