A theorem of Mahler and some applications to transference theorems
I. S. Luthar, M. Vinyard (1977)
Colloquium Mathematicae
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Displaying similar documents to “Mahler's classification of numbers compared with Koksma's”
A theorem of Mahler and some applications to transference theorems
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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.
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The main result of this paper implies that for every positive integer there are at least nonconjugate algebraic numbers which have their Mahler measures lying in the interval . These algebraic numbers are constructed as roots of certain nonreciprocal quadrinomials.