Pell Numbers, Pell-Lucas Numbers and Modular Group

Pell Numbers, Pell-Lucas Numbers and Modular

Group

Q. Mushtaq ;U. Hayat

【期刊名称】《代数集刊（英文版）》 【年(卷),期】2007(014)001

【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. 【总页数】6页(97-102)

【关键词】modular group, Pell numbers, Pell-Lucas numbers, ambiguous numbers, coset diagrams, real quadratic irrational numbers 【作者】Q. Mushtaq ;U. Hayat

【作者单位】Department of Mathematics, Quaid-i-Azam University Islamabad,

Pakistan;Department

of

Mathematics,

Quaid-i-Azam

University Islamabad, Pakistan 【正文语种】中文 【中图分类】O1 【相关文献】

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