Primitive divisors in arithmetic dynamics

DOI10.1017/S0305004108001795zbMath1242.11012arXiv0707.2505MaRDI QIDQ3616234

Patrick Ingram, Joseph H. Silverman

Publication date: 24 March 2009

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.2505

Mathematics Subject Classification ID

Recurrences (11B37) Primes (11A41) Arithmetic dynamics on general algebraic varieties (37P55)

Related Items (30)

Index divisibility in the orbit of 0 for integral polynomials ⋮ Stochastic canonical heights ⋮ Mean divisibility of multinomial coefficients ⋮ 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 ⋮ \(ABC\) implies a Zsigmondy principle for ramification ⋮ Dynamical Belyi maps and arboreal Galois groups ⋮ Using Dynamical Systems to Construct Infinitely Many Primes ⋮ Moduli spaces for dynamical systems with portraits ⋮ The arithmetic of consecutive polynomial sequences over finite fields ⋮ Portraits of preperiodic points for rational maps ⋮ Diophantine approximation and primitive prime divisors in random iterations ⋮ Stability of certain higher degree polynomials ⋮ The 𝐴𝐵𝐶-Conjecture implies uniform bounds on dynamical Zsigmondy sets ⋮ Preperiodic portraits for unicritical polynomials over a rational function field ⋮ Monomial maps on and their arithmetic dynamics ⋮ Finite index theorems for iterated Galois groups of cubic polynomials ⋮ Unnamed Item ⋮ Primitive prime divisors in the critical orbits of one-parameter families of rational polynomials ⋮ On the number of places of convergence for Newton's method over number fields ⋮ Permutation polynomials and factorization ⋮ Primitive divisors, dynamical Zsigmondy sets, and Vojta's conjecture ⋮ Zsigmondy's theorem and primitive divisors of the Lucas and Lehmer sequences in polynomial rings ⋮ Generalized iterations and primitive divisors ⋮ Riccati equations and polynomial dynamics over function fields ⋮ Zsigmondy theorem for arithmetic dynamics induced by a drinfeld module ⋮ Prime factors of dynamical sequences ⋮ Current trends and open problems in arithmetic dynamics ⋮ Primitive prime divisors in backward orbits

Cites Work

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• WANDERING DOMAINS IN NON-ARCHIMEDEAN POLYNOMIAL DYNAMICS
• On the Prime Divisors of the Sequence W _{n +1} = 1 + W ₁ …W _n
• The Galois Theory of Iterates and Composites of Polynomials
• Memoir on Elliptic Divisibility Sequences

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