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

• Autorzy: Peter Bundschuh , Keijo Väänänen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11J91: Transcendence theory of other special functions
• 12F20: Transcendental extensions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 3
• Strony: 239-249

Daty

wydano

2015

Twórcy

autor

Peter Bundschuh

• Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany

autor

Keijo Väänänen

• Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland

Identyfikatory

DOI

10.4064/aa167-3-2