A function field variant of Pillai's problem

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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 G n and H m, defined over F and satisfying some weak conditions, we will prove that the equation G n−H m=f has only finitely many solutions (n,m)∈N 2 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 G n−H m.

Original languageEnglish
Pages (from-to)278-292
Number of pages15
JournalJournal of Number Theory
Volume222
DOIs
Publication statusPublished - May 2021

Fields of Science and Technology Classification 2012

  • 101 Mathematics

Keywords

  • Diophantine equations
  • Linear recurrences
  • Pillai's problem

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