Zhang-Zagier heights of perturbed polynomials

Christophe Doche

Displaying similar documents to “Zhang-Zagier heights of perturbed polynomials”

New methods providing high degree polynomials with small Mahler measure.

Rhin, G., Sac-Épée, J.-M. (2003)

Experimental Mathematics

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The integer transfinite diameter of intervals and totally real algebraic integers

V. Flammang, G. Rhin, C. J. Smyth (1997)

Journal de théorie des nombres de Bordeaux

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In this paper we build on some recent work of Amoroso, and Borwein and Erdélyi to derive upper and lower estimates for the integer transfinite diameter of small intervals $[\frac{r}{s}, \frac{r}{s} + δ]$ , where $\frac{r}{s}$ is a fixed rational and $δ \to 0$ . We also study functions $g_{-}, g, g^{+}$ associated with transfinite diameters of Farey intervals. Then we consider certain polynomials, which we call polynomials, associated to a given interval $I$ . We show how to estimate from below the proportion of roots of an integer polynomial which is sufficiently...

Large integer polynomials in several variables

A. Dubickas (2004)

Rendiconti del Seminario Matematico della Università di Padova

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Pairs of polynomials small at a number to certain algebraic powers

W. Dale Brownawell (1975-1976)

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Root separation for reducible monic quartics

Andrej Dujella, Tomislav Pejković (2011)

Rendiconti del Seminario Matematico della Università di Padova

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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,...

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.