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Rational Hauptmoduls are Replicable

Published online by Cambridge University Press:  20 November 2018

C. J. Cummins  and
S. P. Norton
C. J. Cummins
Affiliation:
Centre Interuniversitaire en Calcul Mathématique Algébrique Department of Mathematics and Statistics Concordia University 1455 de Maisonneuve Boulevard West Montréal, Québec H3G 1M8
S. P. Norton
Affiliation:
Department of Pure Mathematics and Mathematical Statistics Cambridge University16 Mill Lane Cambridge, CB2 1SB England
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Abstract

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It is shown that if ƒ is a Hauptmodul with rational integer coefficients for a group G < PGL2(ℚ)+, of genus zero, containing a with finite index and z ⟼ z+k precisely when k is an integer, then ƒ is replicable. Examples of such functions are given by the Moonshine functions described by Conway and Norton [CN].

Keywords

11F0311F2230F35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 6 , 01 December 1995 , pp. 1201 - 1218
Copyright
Copyright © Canadian Mathematical Society 1995

References

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