Linear equations on Drinfeld modules

Abstract

Let L be a finite extension of the rational function field in one variable over a finite field Fq and E be a Drinfeld module defined over L. Given finitely many elements in E(L), this paper aims to prove that linear relations among these points can be characterized by solutions of an explicitly constructed system of homogeneous linear equations over Fq[t]. As a consequence, we show that there is an explicit upper bound for the size of the generators of linear relations among these points. This result can be regarded as an analogue of a theorem of Masser for finitely many K-rational points on an elliptic curve defined over a number field K.