Volume 33 • Number 2 • 2010   • The Connections Between Continued Fraction Representations of Units and Certain Hecke Groups R. Sahin, S. Ikikardes, Ö. Koruoglu and I. N. Cangül Abstract. Let λ = √D where D is a square free integer such that D = m2 + 1 for m = 1, 3, 4, 5, …, or D = n2 - 1 for n = 2, 3, 4, 5, …. Also, let H(Dλ) be the Hecke group associated to λ. In this paper, we show that the units in H(λ) are infinite pure periodic λ-continued fraction for a certain set of integer D, and hence can not be cusp points. 2000 Mathematics Subject Classification: 20H10, 11K55. Full text: PDF