Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/103993
Title: Quadratic Diophantine equations and two generator Möbius groups
Authors: Tan, E.-C. 
Tan, S.-P. 
Issue Date: Dec-1996
Citation: Tan, E.-C.,Tan, S.-P. (1996-12). Quadratic Diophantine equations and two generator Möbius groups. Journal of the Australian Mathematical Society 61 (3) : 360-368. ScholarBank@NUS Repository.
Abstract: In this paper, we study the set of rational μ in (-2, 2) for which the group Gμ generated by A = (1 μ 0 1), B = (1 0 μ 1) is not free by using quadratic Diophantine equations of the form ax2 - by2 = ±1. We give a new set of accumulation points for rational values of μ in (-2, 2) for which Gμ is not free, thereby extending the results of Beardon where he showed that 1/√N are accumulation points, where N is an integer which is not a perfect square. In particular, we exhibit an infinite set of accumulation points for μ between 1 and 2 including the point 1.
Source Title: Journal of the Australian Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/103993
ISSN: 14467887
Appears in Collections:Staff Publications

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