Multiplicative dependence among iterated values of rational functions modulo finitely generated groups

2018/11/12 by Bérczes, Attila, Ostafe, Alina, Shparlinski, Igor E. +1
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1811.04971

Abstract

We study multiplicative dependence between elements in orbits ofalgebraic dynamical systems over number fields modulo a finitely generated multiplicative subgroup of the field. We obtain a series of results, many of which may be viewed as a blend of Northcott's theorem on boundedness of preperiodic points and Siegel's theorem on finiteness of solutions to S-unit equations.

Related

• On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem
• Multiplicative dependence modulo subsets
• On multiplicative independence of rational function iterates
• Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers
• Reduction of polynomial dynamical systems modulo primes