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
AN - SCOPUS:85054174844
VL - 197
SP - 228
EP - 249
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -