Greenʹs Functions for Drinfeld Modular Curves Original Research Article

LetK=imageq(T) be a rational function field and ∞ the place given by the degree inT. LetL∞/K∞be a finite extension with ramification index not bigger than 2. We show in this paper how the local Néron–Tate height pairing at ∞ on Drinfeld modular curves overKof divisors whose points are defined overL∞can be described through analytic functions onΩ×ΩwhereΩis the Drinfeld upper half plane. The Greenʹs function is locally constant around the cusps. ForX0(N) the Greenʹs function for cusps is then described by Eisenstein series.