Rational 6-cycles under iteration of quadratic polynomials
Number Theory
2009-12-07 v2
Abstract
We present a proof, which is conditional on the Birch and Swinnerton-Dyer Conjecture for a specific abelian variety, that there do not exist rational numbers x and c such that x has exact period N = 6 under the iteration x |-> x^2 + c. This extends earlier results by Morton for N = 4 and by Flynn, Poonen and Schaefer for N = 5.
Cite
@article{arxiv.0803.2836,
title = {Rational 6-cycles under iteration of quadratic polynomials},
author = {Michael Stoll},
journal= {arXiv preprint arXiv:0803.2836},
year = {2009}
}
Comments
15 pages; this is the version that appeared in print