Rational 6-cycles under iteration of quadratic polynomials

Details Rational 6-cycles under iteration of quadratic polynomials Rational 6-cycles under iteration of quadratic polynomials

2008-03-19

arxiv.org/abs/0803.2836v2

London Math. Soc. J. Comput. Math. 11, 367-380 (2008)

Mathematics

Number Theory

15 pages; this is the version that appeared in print

Scientific paper

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.

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