A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems
Number Theory
2010-02-08 v3 Dynamical Systems
Abstract
Fix a rational basepoint b and a rational number c. For the quadratic dynamical system f_c(x) = x^2+c, it has been shown that the number of rational points in the backward orbit of b is bounded independent of the choice of rational parameter c. In this short note we investigate the dependence of the bound on the basepoint b, assuming a strong form of the Mordell Conjecture.
Keywords
Cite
@article{arxiv.0907.4365,
title = {A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems},
author = {X. W. C. Faber},
journal= {arXiv preprint arXiv:0907.4365},
year = {2010}
}
Comments
5 pages; Final version to appear in Comptes Rendus Mathematique