THE CONSTRUCTION OF THE HILBERT GENUS FIELDS OF REAL CYCLIC QUARTIC FIELDS

摘要

Let p be a prime number such that p = 2 or p equivalent to 1 (mod 4). Let epsilon p denote the fundamental unit of Q(root p) and let a be a positive square-free integer. In the present paper, we construct the Hilbert genus field of the real cyclic quartic fields Q(Va epsilon p root p).