Minoration effective de la hauteur des points d'une courbe de $G\_m^2$ définie sur $Q$

Details Minoration effective de la hauteur des points d'une courbe de $G\_m^2$ définie sur $Q$ Minoration effective de la hauteur des points d'une courbe de $G\_m^2$ définie sur $Q$

2005-09-08

arxiv.org/abs/math/0509190v1

Mathematics

Number Theory

28 pages \`{a} para\^{i}tre dans Acta Arithmetica

Scientific paper

We are concerned here with Lehmer's problem in dimension 2 ; we give a lower bound for the height of a non-torsion point of $G\_m^2$ on a non-torsion curve defined over $Q$, depending on the degree of the curve only. We have first been inspired by \cite{Am-Da3}; we develop a new approach, inherent in the dimension two (or more precisely the codimension two), and then obtain a better result where the error's term is improved significantly, moreover we give an explicit expression for the constant.

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