A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems

Details A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems

2009-07-24

arxiv.org/abs/0907.4365v3

Mathematics

Number Theory

5 pages; Final version to appear in Comptes Rendus Mathematique

Scientific paper

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.

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