A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems
Abstract
Fix a rational basepoint b and a rational number c. For the quadratic dynamical system fc(x) = x2+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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