Primitive divisors, dynamical Zsigmondy sets, and Vojta's conjecture

DOI10.1016/j.jnt.2013.03.005zbMath1297.37046arXiv1209.3491OpenAlexW2963202533WikidataQ122940844 ScholiaQ122940844MaRDI QIDQ740846

Joseph H. Silverman

Publication date: 9 September 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.3491

zbMATH Keywords

arithmetic dynamicsprimitive divisorVojta's conjectureZsigmondy set

Mathematics Subject Classification ID

Varieties over global fields (11G35) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) (11J97) Sequences (mod (m)) (11B50) Arithmetic dynamics on general algebraic varieties (37P55) Dynamical systems over global ground fields (37P15)

Related Items (11)

Index divisibility in the orbit of 0 for integral polynomials ⋮ Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups ⋮ Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map ⋮ Squarefree doubly primitive divisors in dynamical sequences ⋮ The 𝐴𝐵𝐶-Conjecture implies uniform bounds on dynamical Zsigmondy sets ⋮ Prime divisors in polynomial orbits over function fields ⋮ An equivariant isomorphism theorem for mod $\mathfrak {p}$ reductions of arboreal Galois representations ⋮ Vojta's conjecture on rational surfaces and the \(abc\) conjecture ⋮ The Vojta conjecture implies Galois rigidity in dynamical families ⋮ Current trends and open problems in arithmetic dynamics ⋮ Integral points and relative sizes of coordinates of orbits in \(\mathbb P^N\)

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