Transcendence measure for η/ω
Transcendence measures of certain numbers whose transcendency was proved by A. Baker
Transcendence measures of exponentials and logarithms of algebraic numbers
Transcendence of certain infinite sums involving rational functions
Transcendence of infinite sums of simple functions
Transcendence of numbers with an expansion in a subclass of complexity 2n + 1
We divide infinite sequences of subword complexity 2n+1 into four subclasses with respect to left and right special elements and examine the structure of the subclasses with the help of Rauzy graphs. Let k ≥ 2 be an integer. If the expansion in base k of a number is an Arnoux-Rauzy word, then it belongs to Subclass I and the number is known to be transcendental. We prove the transcendence of numbers with expansions in the subclasses II and III.
Transcendence of the values of functions satisfying generalized Mahler type functional equations.
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...
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...
Transcendence with Rosen continued fractions
We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.
Transcendental sequences
Transcendentality of zeros of higher derivatives of functions involving Bessel functions.
Transcendenz von e und ....
Transzendente Zahlen als Fourierkoeffizienten von Heckes Modulformen
Transzendenzeigenschaften von Perioden elliptischer Integrale.
Transzendenzmaße in Körpern formaler Laurentreihen.
Travaux récents de G. V. Čudnovskij
Two proofs of transcendency of and
Two results in metrical diophantine approximation
Type de transcendance -adique