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Existence conditions for a class of modular subgroups of genus zero

Published online by Cambridge University Press:  17 April 2009

Joachim A. Hempel
Joachim A. Hempel
Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia e-mail: joachimh@maths.usyd.edu.au
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Every subgroup of finite index of the modular group PSL (2, ℤ) has a signature consisting of conjugacy-invariant integer parameters satisfying certain conditions. In the case of genus zero, these parameters also constitute a prescription for the degree and the orders of the poles of a rational function F with the property:

Functions correspond to subgroups, and we use this to establish necessary and sufficient conditions for existence of subgroups with a certain subclass of allowable signatures.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 517 - 525
Copyright
Copyright © Australian Mathematical Society 2002

References

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