English

Linear equations on Drinfeld modules

Number Theory 2026-05-19 v2

Abstract

Let LL be a finite extension of the rational function field over a finite field Fq\mathbb{F}_q and EE be a Drinfeld module defined over LL. Given finitely many elements in E(L)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]\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 KK-rational points on an elliptic curve defined over a number field KK.

Keywords

Cite

@article{arxiv.2011.00434,
  title  = {Linear equations on Drinfeld modules},
  author = {Yen-Tsung Chen},
  journal= {arXiv preprint arXiv:2011.00434},
  year   = {2026}
}

Comments

added Section 4; corrected few typos; 22 pages

R2 v1 2026-06-23T19:48:58.066Z