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|Title:||Quadratic Diophantine equations and two generator Möbius groups||Authors:||Tan, E.-C.
|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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