Analogs of Delta(z) for Triangular Shimura Curves, by Shujuan Ji

This paper has appeared in Acta Arith. 84 (1998) no. 2, 97-108, and so the dvi version has been removed. In this paper, we construct analogs of the classical \Delta-function for quotients of the upper half plane H by certain arithmetic triangle groups \Gamma coming from quaternion division algebras B. We also establish a relative integrality result concerning modular functions of the form \Delta(\alpha z)/\Delta(z) for \alpha in B^+. We give two explicit examples at the end.

Note: The diagrams may be viewed by using delta.ps.



Shujuan Ji <shujuan@math.columbia.edu>