Linear equations on Drinfeld modules

2020/11/01 by Yen-Tsung Chen, Chen, Yen-Tsung
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2011.00434

openalex publication_date 2020/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L be a finite extension of the rational function field over a finite field \mathbbF_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 \mathbbF_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.

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