Arithmetic properties of 3-cycles of quadratic maps over \(\mathbb{Q}\)

DOI10.1016/j.jnt.2022.01.005OpenAlexW4214775247WikidataQ113870316 ScholiaQ113870316MaRDI QIDQ2161354

Patrick Morton, Serban Raianu

Publication date: 4 August 2022

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

Full work available at URL: https://arxiv.org/abs/2105.07435

zbMATH Keywords

infinite graphperiodic pointHilbert class fieldcubic fieldquadratic map

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Polynomials (irreducibility, etc.) (11R09) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05)

Cites Work

• Finiteness theorems for abelian varieties over number fields.
• The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture
• Cycles of quadratic polynomials and rational points on a genus-2 curve
• A Simple Special Case of Sharkovskii's Theorem
• Arithmetic properties of periodic points of quadratic maps
• Period Three Implies Chaos
• Arithmetic properties of periodic points of quadratic maps, II
• The Galois Theory of Periodic Points of Polynomial Maps
• Polynomial cycles in certain local domains
• Rational Periodic Points of the Quadratic Function Q c (x) = x 2 + c
• Periodic points, multiplicities, and dynamical units.
• Arithmetical study of recurrence sequences
• Computing the Degree of the Modular Parametrization of a Modular Elliptic Curve
• On the Prime Divisors of Polynomials
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