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arXiv · 0907.4365

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

X. W. C. Faber
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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.

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X. W. C. Faber. 2010-02-08. A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems. https://arxiv.org/abs/0907.4365

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