Mahler measures in a cubic field

Artūras Dubickas

Displaying similar documents to “Mahler measures in a cubic field”

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.

The cubics which are differences of two conjugates of an algebraic integer

Toufik Zaimi (2005)

Journal de Théorie des Nombres de Bordeaux

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We show that a cubic algebraic integer over a number field $K,$ with zero trace is a difference of two conjugates over $K$ of an algebraic integer. We also prove that if $N$ is a normal cubic extension of the field of rational numbers, then every integer of $N$ with zero trace is a difference of two conjugates of an integer of $N$ if and only if the $3 -$ adic valuation of the discriminant of $N$ is not $4 .$

The mean values of logarithms of algebraic integers

Artūras Dubickas (1998)

Journal de théorie des nombres de Bordeaux

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Let $α$ be an algebraic integer of degree $d$ with conjugates $α_{1} = α, α_{2}, \dots, α_{d}$ . In the paper we give a lower bound for the mean value $M_{p} (α) = \sqrt[p]{\frac{1}{d} \sum_{i = 1}^{d} | log | α_{i} {| |}^{p}}$ when $α$ is not a root of unity and $p > 1$ .

Exceptional units and numbers of small Mahler measure.

Silverman, Joseph H. (1995)

Experimental Mathematics

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On Roots of Polynomials with Positive Coefficients

Toufik Zaïmi (2011)

Publications de l'Institut Mathématique

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