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.