Principal moduli and class fields

Abstract

We study the values taken by Gamma_0(n) modular functions at elliptic points of order 2 for the Fricke extension that lie outside Gamma_0(n). In the case of a principal modulus (`Hauptmodul') for Gamma_0(n) or its Fricke extension, we determine the class fields generated by these values.

15 pages AMS-LaTeX