Let K = $ k(\sqrt \theta ) $ be a real cyclic quartic field, k be its quadratic subfield and $ \tilde K = k(\sqrt { - \theta } ) $ be the corresponding imaginary quartic field. Denote the class numbers of K, k and $ \tilde K $ by h K , h k and {417-3} respectively. Here congruences modulo powers of 2 for h ? = h K /h K and $ \tilde h^ - = h_{\tilde K} /h_k $ are obtained via studying the p-adic L-functions of the fields.
