ON THE DRINFELD DISCRIMINANT FUNCTION

The discriminant function Delta is a certain rigid analytic modular fo rm defined on Drinfeld's upper half-plane Omega. Its absolute value \D elta\ may be considered as a function on the associated Bruhat-Tits tr ee T. We compare log \Delta\ with the conditionally convergent complex -valued Eisenstein series E defined on T and thereby obtain results ab out the growth of \Delta\ and of some related modular forms. We furthe r determine to what extent roots may be extracted of Delta(z)/Delta(nz ), regarded as a holomorphic function on Omega. In some cases, this en ables us to calculate cuspidal divisor class groups of modular curves.