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PRINCIPAL MODULI AND CLASS FIELDS

Published online by Cambridge University Press:  23 December 2003

DAVID COX ,
JOHN McKAY  and
PETER STEVENHAGEN
DAVID COX
Affiliation:
Department of Mathematics and Computer Science, Amherst College, Amherst, MA 01002-5000, USAdac@cs.amherst.edu
JOHN McKAY
Affiliation:
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve West, Montréal, Québec, H3G 1M8, Canadamckay@cs.concordia.ca
PETER STEVENHAGEN
Affiliation:
Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, The Netherlandspsh@math.leidenuniv.nl
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Abstract

The values taken by $\Gamma_0(n)$-modular functions at elliptic points of order 2 for the Fricke group $\Gamma_0(n)^\dagger$ that lie outside $\Gamma_0(n)$ are studied. In the case of a principal modulus (‘Hauptmodul’) for $\Gamma_0(n)$ or $\Gamma_0(n)^\dagger$, the class fields generated by these values are determined.

Keywords

11R37 (primary)11G1520H10 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 1 , January 2004 , pp. 3 - 12
Copyright
© The London Mathematical Society 2004

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