On Lower Bounds for Polynomials in the Values of E-Functions.
On linear forms of a certain class of G-functions and p-adic G-functions
Arithmetical investigations of a certain infinite product
Transcendence results on the generating functions of the characteristic functions of certain self-generating sets
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. Then, a Roth-type...
Linear independence of certain Lambert and allied series
Transcendence results on the generating functions of the characteristic functions of certain self-generating sets, II
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...
Algebraic independence of the generating functions of Stern’s sequence and of its twist
Very recently, the generating function of the Stern sequence , defined by and for any integer , has been considered from the arithmetical point of view. Coons [
Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré
On the non-quadraticity of values of the q-exponential function and related q-series
On Siegel-Shidlovskii's theory for q-difference equations
Page 1