Displaying similar documents to “Constants for lower bounds for linear forms in the logarithms of algebraic numbers I. The general case”

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

Peter Bundschuh, Keijo Väänänen (2014)

Acta Arithmetica

Similarity:

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....

A generalization of a theorem of Schinzel

Georges Rhin (2004)

Colloquium Mathematicae

Similarity:

We give lower bounds for the Mahler measure of totally positive algebraic integers. These bounds depend on the degree and the discriminant. Our results improve earlier ones due to A. Schinzel. The proof uses an explicit auxiliary function in two variables.