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Modular Equations and Discrete, Genus-Zero Subgroups of SL(2, ℝ) Containing Γ(N)

Published online by Cambridge University Press:  20 November 2018

C. J. Cummins
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Abstract

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Let $G$ be a discrete subgroup of $\text{SL}\left( 2,\,\mathbb{R} \right)$ which contains $\Gamma \left( N \right)$ for some $N$. If the genus of $X\left( G \right)$ is zero, then there is a unique normalised generator of the field of $G$-automorphic functions which is known as a normalised Hauptmodul. This paper gives a characterisation of normalised Hauptmoduls as formal $q$ series using modular polynomials.

Keywords

11F0311F2230F35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 36 - 45
Copyright
Copyright © Canadian Mathematical Society 2002

Footnotes

The author was supported by NSERC and FCAR grants.

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