The connections between continued fraction representations of units and certain hecke groups

Abstract

Let lambda = root D where D is a square free integer such that D = m(2)+1 for m = 1,3, 4, 5,..., or D = n(2) - 1 form = 2, 3, 4, 5,.... Also, let H(lambda) be the Hecke group associated to A. In this paper, we show that the units in H(lambda) are infinite pure periodic lambda-continued fraction for a certain set of integer D, and hence can not be cusp points.