Ernst-Ulrich Gekeler

Drinfeld modular curves

Notations.- Drinfeld modules.- Lattices.- Partial zeta functions.- Drinfeld modules of rank 1.- Modular curves over C.- Expansions around cusps.- Modular forms and functions.- Complements.

On the Drinfeld discriminant function

The discriminant function Δ is a certain rigid analytic modularform defined on Drinfeld’s upper half-plane Ο. Its absolutevalue ❘Δ❘ may be considered as a function on theassociated Bruhat–Tits tree T. We compare log ❘Δ❘ with the conditionally convergent complex-valued Eisenstein series Edefined on T and thereby obtain results about the growth of ❘Δ❘ and of some related modular forms. We further determine to what extent roots may be extracted of Δ(z)/Δ(nz),regarded as a holomorphic function on Ο. In some cases, this enables us to calculate cuspidal divisor class groups of modular curves.

Some observations on the arithmetic of Eisenstein series for the modular group SL(2, \Bbb Z)

Abstract. For even integers

A note on the finiteness of certain cuspidal divisor class groups

k\geqq4

Frobenius distributions of Drinfeld modules over finite fields

, let

On the zeroes of Goss polynomials

\varphi_k(X)

ZERO DISTRIBUTION AND DECAY AT INFINITY OF DRINFELD MODULAR COEFFICIENT FORMS

be the separable rational polynomial that encodes the j-invariants of non-elliptic zeroes of the Eisenstein series Ek for the modular group SL

Towers of GL(

(2,{Bbb Z})

r

. We prove Kummer-type congruence properties for the

)-type of modular curves

\varphi_k