Classes et unités des extensions cycliques réelles de degré 4 de ${\bf Q}$

Abstract

Let K be a real cyclic extension of degree 4 of Q ; let k be its quadratic subfield. We determine the class number and the units of K, and we prove that the problem of the “capitulation” of classes of k in K is characterized by elementary properties of the units of K. We have obtained a numerical table of the class number, the units, and the eventual “capitulation” of a class, for all fields K with conductor f<4000 ; we publish here an extract of it.