Linear equations on Drinfeld modules
Number Theory
2026-05-19 v2
Abstract
Let be a finite extension of the rational function field over a finite field and be a Drinfeld module defined over . Given finitely many elements in , 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 . 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 -rational points on an elliptic curve defined over a number field .
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