Transcendence, automata theory and gamma functions for polynomial rings
Transcendence measure for η/ω
Transcendence measures for continued fractions involving repetitive or symmetric patterns
There is a long tradition in constructing explicit classes of transcendental continued fractions and especially transcendental continued fractions with bounded partial quotients. By means of the Schmidt Subspace Theorem, existing results were recently substantially improved by the authors in a series of papers, providing new classes of transcendental continued fractions. It is the purpose of the present work to show how the Quantitative Subspace Theorem yields transcendence measures for (most of)...
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 Artin-Mazur zeta function for polynomial maps of 𝔸¹(𝔽̅ₚ)
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.
Transcendency of Local Conjugacies in Complex Dynamics and Transcendency of their Values.
Transcendental numbers having explicit -adic and Jacobi-Perron expansions
Transcendental sequences
Transcendental values of the p-adic digamma function
Transcendentality of zeros of higher derivatives of functions involving Bessel functions.
Transcendenz von e und ....
Transendenceand algebraic independence of Liouville-like numbers