Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups

DOI10.1093/imrn/rnz091zbMath1490.37115arXiv1811.04971OpenAlexW2901832352WikidataQ128115831 ScholiaQ128115831MaRDI QIDQ5068164

Joseph H. Silverman, Alina Ostafe, Attila Bérczes, Igor E. Shparlinski

Publication date: 5 April 2022

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.04971

zbMATH Keywords

Weil heightalgebraic dynamical system

Mathematics Subject Classification ID

Heights (11G50) Exponential Diophantine equations (11D61) Global ground fields in algebraic geometry (14G25) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30)

Related Items (8)

On abelian points of varieties intersecting subgroups in a torus ⋮ A fusion variant of the classical and dynamical Mordell-Lang conjectures in positive characteristic ⋮ On effective \(\epsilon\)-integrality in orbits of rational maps over function fields and multiplicative dependence ⋮ Diophantine approximations. Abstracts from the workshop held April 17--23, 2022 ⋮ Rational dynamical systems, \(S\)-units, and \(D\)-finite power series ⋮ Unlikely intersections over finite fields: polynomial orbits in small subgroups ⋮ On the maximum modulus of integers in Kummer extensions ⋮ Cyclotomic preperiodic points for morphismsin affine spaces and preperiodic points with bounded house and height

Cites Work

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• Integral points in two-parameter orbits
• A quantitative estimate for quasiintegral points in orbits
• Primitive divisors, dynamical Zsigmondy sets, and Vojta's conjecture
• Finiteness theorems for abelian varieties over number fields.
• Integer points, diophantine approximation, and iteration of rational maps
• On multiplicative dependence of values of rational functions and a generalization of the Northcott theorem
• Uniform boundedness of \(S\)-units in arithmetic dynamics
• \(ABC\) implies a Zsigmondy principle for ramification
• Periodic points on an algebraic variety
• Effective results for hyper- and superelliptic equations over number fields
• ABC implies primitive prime divisors in arithmetic dynamics
• Primitive Prime Divisors in Zero Orbits of Polynomials
• Prime factors of dynamical sequences
• On primitive divisors of n² + b
• Primitive Prime Divisors in the Critical Orbit of zd+c
• Primitive divisors in arithmetic dynamics
• On the equation $y^m = P(x)$
• Squarefree doubly primitive divisors in dynamical sequences
• Orbits of Algebraic Dynamical Systems in Subgroups and Subfields

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