Pell Numbers, Pell-Lucas Numbers and Modular Group

• 来源期刊: 代数集刊（英文版）
• 关键词: modular group Pell numbers Pell-Lucas numbers ambiguous numbers coset diagrams real quadratic irrational numbers
• 年，卷（期）: 2007,（1）
• 页码范围: 97-102
• 页数: 6页
• 语种: 英文

摘要

We show that the matrix A(g), representing the element g = ((xy)2(xy2)2)m (m≥) of the modular group PSL(2,Z)=(x,y:x2=y3=1),where x:z →-1/z and y :z → -1/z, is a 2×2 symmetric matrix whose entries are Pell numbers and whose trace is a Pell-Lucas number. If g fixes elements of Q(√d), where d is a square-free positive number, on the circuit of the coset diagram, then d ＝ 2 and there are only four pairs of ambiguous numbers on the circuit.