Displaying similar documents to “On the height of algebraic numbers with real conjugates”

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.

Comments on the height reducing property

Shigeki Akiyama, Toufik Zaimi (2013)

Open Mathematics

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A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one,...

Algebraic S-integers of fixed degree and bounded height

Fabrizio Barroero (2015)

Acta Arithmetica

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Let k be a number field and S a finite set of places of k containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of S-integers of k. Moreover, we give an asymptotic formula for the number of S̅-integers of bounded height and fixed degree over k, where S̅ is the set of places of k̅ lying above the ones in S.

Higher Mahler measure of an n-variable family

Matilde N. Lalín, Jean-Sébastien Lechasseur (2016)

Acta Arithmetica

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We prove formulas for the k-higher Mahler measure of a family of rational functions with an arbitrary number of variables. Our formulas reveal relations with multiple polylogarithms evaluated at certain roots of unity.