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Displaying similar documents to “On the transcendence of certain power series 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....