Displaying similar documents to “A theorem of Mahler and some applications to transference theorems”

A generalization of a theorem of Schinzel

Georges Rhin (2004)

Colloquium Mathematicae

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We give lower bounds for the Mahler measure of totally positive algebraic integers. These bounds depend on the degree and the discriminant. Our results improve earlier ones due to A. Schinzel. The proof uses an explicit auxiliary function in two variables.

Nonreciprocal algebraic numbers of small measure

Artūras Dubickas (2004)

Commentationes Mathematicae Universitatis Carolinae

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The main result of this paper implies that for every positive integer d ⩾ 2 there are at least ( d - 3 ) 2 / 2 nonconjugate algebraic numbers which have their Mahler measures lying in the interval ( 1 , 2 ) . These algebraic numbers are constructed as roots of certain nonreciprocal quadrinomials.