Effective results on the Skolem Problem for linear recurrence sequences

Min Sha

doi:10.1016/j.jnt.2018.08.012

Effective results on the Skolem Problem for linear recurrence sequences

Min Sha

Department of Computing

Research output: Contribution to journal › Article

3 Citations (Scopus)

Abstract

In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond which every term of the sequence is non-zero. It turns out that this case covers almost all such sequences whose coefficients are rational numbers.

Original language	English
Pages (from-to)	228-249
Number of pages	22
Journal	Journal of Number Theory
Volume	197
DOIs	https://doi.org/10.1016/j.jnt.2018.08.012
Publication status	Published - Apr 2019

Keywords

Height
Linear form in logarithms
Linear recurrence sequence
The Skolem Problem

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AB - In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond which every term of the sequence is non-zero. It turns out that this case covers almost all such sequences whose coefficients are rational numbers.

KW - Height

KW - Linear form in logarithms

KW - Linear recurrence sequence

KW - The Skolem Problem

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UR - http://purl.org/au-research/grants/arc/DP130100237

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JF - Journal of Number Theory

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