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Quadratic Diophantine equations and two generator Möbius groups

Published online by Cambridge University Press:  09 April 2009

Eng-Chye Tan  and
Ser-Peow Tan
Ser-Peow Tan
Affiliation:
Department of Mathematics Faculty of Science National University of Singapore 10 Kent Ridge Crescent Singapore 0511 e-mail: [email protected] and [email protected]
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Abstract

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In 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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 3 , December 1996 , pp. 360 - 368
Copyright
Copyright © Australian Mathematical Society 1996

References

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