Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-22T20:08:20.351Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

REFERENCES

1.Hecke, E., Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichungen, Math. Ann. 112 (1935), 664–699.CrossRefGoogle Scholar
2.Hutchinson, J. T., On automorphic groups whose coefficients are integers in a quadratic field, Trans. American Math. Soc. 7 (1906), 530–536.CrossRefGoogle Scholar
3.Peterssoa, H., Konstruktion der Modulformen und der zu gewissen Grenzkreisgruppen gehorigen automorphen Formen von positiver reeller Dimension und die vollstandige Bestimmung ihrer Fourierkoeffizienten, S.-B. Heidelberger Akad. Wiss. (1950), 417–494.CrossRefGoogle Scholar
4.Rankin, R. A., On horocyclic groups, Proc. London Math. Soc. (3) 4 (1954), 220–234.Google Scholar
5.Rosen, D., A class of continued fractions associated with certain properly discontinuous groups, Duke Math. J. 21 (1954), 549–564.CrossRefGoogle Scholar
6.Vorob'ev, N. N., Fibonacci numbers (London, 1961). Translated by Moss, H..Google Scholar