Lower bounds of heights of points on hypersurfaces
نویسنده
چکیده
Let us first recall Lehmer’s conjecture [Le] on lower bounds for the height of an algebraic number which was stated in 1933. Let K be an algebraic number field of degree D over Q. For any valuation v we denote Dv = [Kv : Qv], where Kv,Qv are the completions of K,Q with respect to v. For archimedean v we normalise the valuation by |xv| = |x|Dv/D where |.| is the ordinary complex absolute value. When v is non-archimedean we take |p|v = p−Dv/D where p is the unique rational prime such that |p|v < 1. The height of an algebraic number α ∈ K is defined by H(α) = ∏
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