On the size of a linear combination of two linear recurrence sequences over function fields

Sebastian Heintze

doi:10.1007/s10998-023-00515-8

On the size of a linear combination of two linear recurrence sequences over function fields

Sebastian Heintze^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

Let G_n and H_m be two non-degenerate linear recurrence sequences defined over a function field F in one variable over C, and let μ be a valuation on F. We prove that under suitable conditions there are effectively computable constants c₁ and C^′ such that the bound μ(Gn-Hm)≤μ(Gn)+C′holds for max (n, m) > c₁.

Original language	English
Pages (from-to)	283-292
Number of pages	10
Journal	Periodica Mathematica Hungarica
Volume	87
Issue number	2
Early online date	13 Apr 2023
DOIs	https://doi.org/10.1007/s10998-023-00515-8
Publication status	Published - Dec 2023

Keywords

Growth
Linear recurrence sequence

ASJC Scopus subject areas

General Mathematics

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10.1007/s10998-023-00515-8Licence: CC BY 4.0

s10998-023-00515-8Final published version, 233 KBLicence: CC BY 4.0

Cite this

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AB - Let Gn and Hm be two non-degenerate linear recurrence sequences defined over a function field F in one variable over C, and let μ be a valuation on F. We prove that under suitable conditions there are effectively computable constants c1 and C′ such that the bound μ(Gn-Hm)≤μ(Gn)+C′holds for max (n, m) > c1.

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KW - Linear recurrence sequence

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On the size of a linear combination of two linear recurrence sequences over function fields

Abstract

Keywords

ASJC Scopus subject areas

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