Effective results on the Skolem Problem for linear recurrence sequences

JOURNAL OF NUMBER THEORY

卷:197

Article

Sha, Min¹ 

[1] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia

关键词: Linear recurrence sequence;    The Skolem Problem;    Height;    Linear form in logarithms;   

DOI  :  10.1016/j.jnt.2018.08.012

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free