On the Fundamental Units and a Lower Estimate of the Class Numbers of Certain Real Quadratic Fields

Abstract

We give explicitly the fundamental units of real quadratic fields over the rationalsQ , which is distinct from RD type. H. Yokoi and the second author have found an explicit expression of the fundamental units of certain real quadratic fields K, which intersect trivially to RD type, an Extended RD and a Generalized RD one. Using the formula of the fundamental units, we give a lower estimate of the class numbers of these fields and determine the positive density of such fields K.