Consider a non-Galois cubic extension K/Q ramified at a single prime p > 3. We show that if K is a subfield of an S_4-extension L/Q ramified only at p, we can determine the Artin conductor of the projective representation associated to L/Q, which is based on whether or not K/Q is totally real. We also show that the number of S_4-extensions of this type with K as a subfield is of the form 2^n - 1 for some n >= 0. If K/Q is totally real, n > 1. This proves two conjectures of Siman Wong.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Childers, Kevin Ronald, "Octahedral Extensions and Proofs of Two Conjectures of Wong" (2015). All Theses and Dissertations. 5314.
octahedral, Galois representations, number fields