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Abstrakty
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 statement is due to Adamczewski, whereas the second is our previous main result. Moreover, an arithmetical consequence of the transcendence degree claim is that, for any algebraic α with 0 < |α| < 1, the field ℚ(F(α),F(α⁴),G(α),G(α⁴)) has transcendence degree 3 over ℚ.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
239-249
Opis fizyczny
Daty
wydano
2015
Twórcy
autor
- Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany
autor
- Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland
Bibliografia
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-3-2