Arithmetic implications of the distribution of integral zeros of exponential polynomials
Alfred J. Van der Poorten (1974-1975)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Alfred J. Van der Poorten (1974-1975)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Peter Bundschuh, Keijo Väänänen (2014)
Acta Arithmetica
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This article continues two papers which recently appeared in this same journal. First, Dilcher and Stolarsky [140 (2009)] introduced two new power series, F(z) and G(z), related to the so-called Stern polynomials and having coefficients 0 and 1 only. Shortly later, Adamczewski [142 (2010)] proved, inter alia, that G(α),G(α⁴) are algebraically independent for any algebraic α with 0 < |α| < 1. Our first key result is that F and G have large blocks of consecutive zero coefficients....
Artūras Dubickas (1998)
Journal de théorie des nombres de Bordeaux
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Let be an algebraic integer of degree with conjugates . In the paper we give a lower bound for the mean value when is not a root of unity and .
Thomas Töpfer (1995)
Compositio Mathematica
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Peter Bundschuh, Keijo Väänänen (2015)
Acta Arithmetica
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This article continues a previous paper by the authors. Here and there, the two power series F(z) and G(z), first introduced by Dilcher and Stolarsky and related to the so-called Stern polynomials, are studied analytically and arithmetically. More precisely, it is shown that the function field ℂ(z)(F(z),F(z⁴),G(z),G(z⁴)) has transcendence degree 3 over ℂ(z). This main result contains the algebraic independence over ℂ(z) of G(z) and G(z⁴), as well as that of F(z) and F(z⁴). The first...
Artūras Dubickas (2004)
Commentationes Mathematicae Universitatis Carolinae
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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.
P. Cijsouw, R. Tijdeman (1973)
Acta Arithmetica
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K. Orlov, B. Savić (1983)
Matematički Vesnik
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