Displaying similar documents to “A generalization of a theorem of Schinzel”

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

Peter Bundschuh, Keijo Väänänen (2014)

Acta Arithmetica


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....

Nonreciprocal algebraic numbers of small measure

Artūras Dubickas (2004)

Commentationes Mathematicae Universitatis Carolinae


The main result of this paper implies that for every positive integer d 2 there are at least ( d - 3 ) 2 / 2 nonconjugate algebraic numbers which have their Mahler measures lying in the interval ( 1 , 2 ) . These algebraic numbers are constructed as roots of certain nonreciprocal quadrinomials.

Totally positive algebraic integers of small trace

Chistopher J. Smyth (1984)

Annales de l'institut Fourier


Let α be a totally positive algebraic integer, with the difference between its trace and its degree at most 6. We describe an algorithm for finding all such α , and display the resulting list of 1314 values of α which the algorithm produces.

Lower Bounds on the Directed Sweepwidth of Planar Shapes

Markov, Minko, Haralampiev, Vladislav, Georgiev, Georgi (2015)

Serdica Journal of Computing


We investigate a recently introduced width measure of planar shapes called sweepwidth and prove a lower bound theorem on the sweepwidth.