Abstract
AbstractIn this paper, we study the set of rational μ in (−2, 2) for which the group Gu generated by 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 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.
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Schedule a callMore From: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
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