A function field variant of Pillai's problem

2020/12/29 by Clemens Fuchs, Sebastian Heintze · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Algebraic Geometry and Number Theory #Analytic Number Theory Research

paper · doi:10.1016/j.jnt.2020.11.004

Abstract

In this paper, we consider a variant of Pillai's problem over function fields F in one variable over C. For given simple linear recurrence sequences Gn and Hm, defined over F and satisfying some weak conditions, we will prove that the equation Gn−Hm=f has only finitely many solutions (n,m)∈N2 for any non-zero f∈F, which can be effectively bounded. Furthermore, we prove that under suitable assumptions there are only finitely many effectively computable f with more than one representation of the form Gn−Hm.

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• Quantitative growth of multi-recurrences

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