On the Drinfeld discriminant function

The discriminant function is a certain rigid analytic modularform defined on Drinfelds upper half-plane . Its absolutevalue may be considered as a function on theassociated Bruhat–Tits tree T. We compare log with the conditionally convergent complex-valued Eisenstein series Edefined on T and thereby obtain results about the growth of and of some related modular forms. We further determine to what extent roots may be extracted of (z)/(nz),regarded as a holomorphic function on . In some cases, this enables us to calculate cuspidal divisor class groups of modular curves.