论文标题
Drinfeld模块上的线性方程
Linear equations on Drinfeld modules
论文作者
论文摘要
令$ l $是有限字段$ \ mathbb {f} _q $和$ e $的有限扩展，是定义在$ L $上的Drinfeld模块。鉴于$ e（l）$中有限的许多元素，本文旨在证明这些点之间的线性关系可以通过$ \ mathbb {f} _q [t] $的明确构造的均质线性方程式的解决方案来表征。结果，我们表明，这些点之间线性关系的发电机的大小有明确的上限。该结果可以被视为Masser定理的类似物，以有限的$ K $合理点在数字$ k $上定义的椭圆曲线上有限。
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 $K$.
