TY - JOUR

T1 - Effective results on the Skolem Problem for linear recurrence sequences

AU - Sha, Min

PY - 2019/4

Y1 - 2019/4

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85054174844&partnerID=8YFLogxK

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

U2 - 10.1016/j.jnt.2018.08.012

DO - 10.1016/j.jnt.2018.08.012

M3 - Article

VL - 197

SP - 228

EP - 249

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -