Ray Class Fields of Conductor p

Assume the generalized Riemann hypothesis holds. This thesis proves that a totally real multiquadratic number field K has a positive density of integral primes p for which the ray class field of conductor p has an explicit description as the Hilbert class field of K adjoin the real part of a primitive p-th root of unity if and only if K contains a unit of norm -1. The proof proceeds by first reformulating the question for all Galois number fields algebraically into a question about a set of Frobenius elements in certain field extensions of K. It is then solved for multiquadratic fields assuming the generalized Riemann hypothesis using techniques from analytic number theory. These techniques are an adaptation of Christopher Hooley's conditional proof of Artin's conjecture for primitive roots. The question of which multiquadratic fields contain units of norm -1 is also addressed. It is proven that a multiquadratic field of degree eight or more with odd class number has no unit of norm -1.