Displaying similar documents to “Asymptotic distribution and symmetric means of algebraic numbers”

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....

A unified approach to compact symmetric spaces of rank one

Adam Korányi, Fulvio Ricci (2010)

Colloquium Mathematicae

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A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.

Multiplicative dependence of shifted algebraic numbers

Paulius Drungilas, Artūras Dubickas (2003)

Colloquium Mathematicae

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We show that the set obtained by adding all sufficiently large integers to a fixed quadratic algebraic number is multiplicatively dependent. So also is the set obtained by adding rational numbers to a fixed cubic algebraic number. Similar questions for algebraic numbers of higher degrees are also raised. These are related to the Prouhet-Tarry-Escott type problems and can be applied to the zero-distribution and universality of some zeta-functions.