A remark on the effective Mordell Conjecture and rational pre-images under quadratic dynamical systems

作者：Faber X W C^*

来源：Comptes Rendus Mathematique, 2010, 348(7-8): 355-358.

DOI：10.1016/j.crma.2010.02.010

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.

• 出版日期2010-4