TY - JOUR
T1 - On multiplicative dependence of values of rational functions and a generalization of the Northcott theorem
AU - Ostafe, Alina
AU - Sha, Min
AU - Shparlinski, Igor E.
AU - Zannier, Umberto
PY - 2019/6
Y1 - 2019/6
N2 - In this paper, we study multiplicative dependence of values of polynomials or rational functions over a number field. As an application, we obtain new results on multiplicative dependence in the orbits of a univariate polynomial dynamical system. We also obtain a generalization of the Northcott theorem replacing the finiteness of preperiodic points from a given number field by the finiteness of algebraic integers having two multiplicatively dependent elements in their orbits.
AB - In this paper, we study multiplicative dependence of values of polynomials or rational functions over a number field. As an application, we obtain new results on multiplicative dependence in the orbits of a univariate polynomial dynamical system. We also obtain a generalization of the Northcott theorem replacing the finiteness of preperiodic points from a given number field by the finiteness of algebraic integers having two multiplicatively dependent elements in their orbits.
UR - http://purl.org/au-research/grants/arc/DP180100201
UR - http://purl.org/au-research/grants/arc/DP170100786
UR - http://www.scopus.com/inward/record.url?scp=85069637267&partnerID=8YFLogxK
U2 - 10.1307/mmj/1556589745
DO - 10.1307/mmj/1556589745
M3 - Article
SN - 0026-2285
VL - 68
SP - 385
EP - 407
JO - Michigan Mathematical Journal
JF - Michigan Mathematical Journal
IS - 2
ER -