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An arithmetic characterization of the parabolic points of G(2cos π/5)

Published online by Cambridge University Press:  18 May 2009

David Rosen
David Rosen
Affiliation:
The University Glasgow
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By the group G(2 cos π/q) we mean the group of linear fractional transformations of the complex plane onto itself, generated by V(z)= — 1/z and U(z) = z+λq, where λq = 2 cos (π/q), qbeing a positive integer greater than 2. In this paper we shall be concerned only with the group given by q = 5, and we shall therefore omit the subscript 5 on the λ. We note that λ = λ5 satisfies the equation

x2–x–l=0;(1)

henceλ = (l + 5½)/2.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 2 , July 1963 , pp. 88 - 96
Copyright
Copyright © Glasgow Mathematical Journal Trust 1963

References

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