Explicit lower bounds for the height in Galois extensions of number fields
Copyright policy )Explicit lower bounds for the height in Galois extensions of number fields
Amoroso and Masser proved that for every real ϵ>0, there exists a constant c(ϵ)>0, with the property that, for every algebraic number α such that ℚ(α)/ℚ is a Galois extension, the height of α is either 0 or at least c(ϵ)[ℚ(α):ℚ] -ϵ . In the present article, we establish an explicit version of the aforementioned theorem.
11G50, Mathematics - Number Theory, Height bounds, Galois extensions, FOS: Mathematics, Lehmer's problem, Number Theory (math.NT), [MATH]Mathematics [math], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], 510, 004
11G50, Mathematics - Number Theory, Height bounds, Galois extensions, FOS: Mathematics, Lehmer's problem, Number Theory (math.NT), [MATH]Mathematics [math], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], 510, 004
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