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2023/102/3-4 (10) — DOI: 10.5486/PMD.2023.9439 — pp. 429-437

$S$-unit values of $G_n+G_m$ in function fields

Authors: Sebastian Heintze

Abstract:

In this paper, we consider a simple linear recurrence sequence $G_n $ defined over a function field in one variable over the field of complex numbers. We prove an upper bound on the indices $n$ and $m$ such that $G_n+G_m$ is an $S$-unit. This is a function field analogue of already known results in number fields.

Keywords: linear recurrences, $S$-units

Mathematics Subject Classification: 11B37