Algebraic independence of the numbers $\prod ^ \infty _ {K = 0} (1-p^{-2^{K}})$ with $p$ prime

Kenneth K. Kubota

Displaying similar documents to “Algebraic independence of the numbers $\prod_{K = 0}^{\infty} (1 - p^{- 2^{K}})$ with $p$ prime”

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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Transcendence results on the generating functions of the characteristic functions of certain self-generating sets

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....

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 $p > 1$ .

An axiomatization of Nesterenko's method and applications on Mahler functions II

Thomas Töpfer (1995)

Compositio Mathematica

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Transcendence results on the generating functions of the characteristic functions of certain self-generating sets, II

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...

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.

On the transcendence of certain power series of algebraic numbers

P. Cijsouw, R. Tijdeman (1973)

Acta Arithmetica

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General method for solving transcendental and algebraic equations by means of residuals

K. Orlov, B. Savić (1983)

Matematički Vesnik

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Displaying similar documents to “Algebraic independence of the numbers ∏ K = 0 ∞ ( 1 - p - 2 K ) with p prime”

Displaying similar documents to “Algebraic independence of the numbers $\prod_{K = 0}^{\infty} (1 - p^{- 2^{K}})$ with $p$ prime”