A lower bound for the height in abelian extensions
It is shown that if \(\alpha\neq 0\) is an element which is not a root of unity, of an abelian extension of the rationals, then its logarithmic height, \(h(\alpha)\) satisfies \(h(\alpha)\geq(\log 5)/12\). This is used to obtain lower bounds for norms and class-numbers in abelian extensions.
scientific article; zbMATH DE number 1423159