Linear equations on Drinfeld modules

Abstract

Let $L$ be a finite extension of the rational function field over a finite field ${\mathbb{F}}_q$ 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 ${\mathbb{F}}_q[t]$. 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 $K$.

added Section 4; corrected few typos; 22 pages

References in corpus (1)

• Hyperderivatives of periods and quasi-periods for Anderson $t$-modules

Cited by in corpus (1)

• Linear relations among algebraic points on tensor powers of the Carlitz module