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Rational 6-Cycles Under Iteration of Quadratic Polynomials

Published online by Cambridge University Press:  01 February 2010

Michael Stoll
Michael Stoll
Affiliation:
Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany, Michael.Stoll@uni-bayreuth.de

Abstract

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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 ↦ x2 + c. This extends earlier results by Morton for N = 4 and by Flynn, Poonen and Schaefer for N = 5.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 11 , 2008 , pp. 367 - 380
Copyright
Copyright © London Mathematical Society 2008

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Supplementary material: File

JCM 11 Stoll Appendix A

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