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

Martin Orr

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arXiv · 2607.09565

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

Martin Orr

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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.

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Martin Orr. 2026-07-10. Explicit height bounds for G-functions and unlikely intersections with lines in tori. https://arxiv.org/abs/2607.09565

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