Dyadic Ramification and Quartic Number Fields Original Research Article

Let E = image(√σ) be a quartic number field defined by the irreducible trinomial x4 + bx2 + d with integral coefficients and root √σ. Using Weil′s additive character γp of the rational Witt ring we provide reasonable criteria, in terms of the coefficients b, d of x4 + bx2 + d for the rational prime 2 to ramify in E. Also, we discuss applications of the result to fundamental units in real quadratic subfields.