Explicit height bounds for G-functions and unlikely intersections with lines in tori

Martin Orr

Explicit height bounds for G-functions and unlikely intersections with lines in tori

Number Theory 2026-07-10 v1

Authors: Martin Orr

Abstract

This paper computes explicit constants in Bombieri and Andr\'e's height bound for points at which there are unexpected "global" polymomial relations between values of G-functions. It applies these bounds for G-functions to obtain explicit height bounds for unlikely intersections with lines in tori, making explicit a weak version of the bounded height theorem of Bombieri, Masser and Zannier and, in some cases, improving an explicit bound of Habegger.

Keywords

G-functions height bounds unlikely intersections tori Bombieri-André theorem Bombieri-Masser-Zannier theorem

Cite

@article{arxiv.2607.09565,
  title  = {Explicit height bounds for G-functions and unlikely intersections with lines in tori},
  author = {Martin Orr},
  journal= {arXiv preprint arXiv:2607.09565},
  year   = {2026}
}

Comments

38 pages