Displaying similar documents to “On the binary expansion of irrational algebraic numbers”

Quantitative versions of the Subspace Theorem and applications

Yann Bugeaud (2011)

Journal de Théorie des Nombres de Bordeaux

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During the last decade, several quite unexpected applications of the Schmidt Subspace Theorem were found. We survey some of these, with a special emphasize on the consequences of quantitative statements of this theorem, in particular regarding transcendence questions.

Diophantine approximation and special Liouville numbers

Johannes Schleischitz (2013)

Communications in Mathematics

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This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers ζ 1 , ζ 2 , ... , ζ k . The approach relies on results on the connection between the set of all s -adic expansions ( s ≥ 2 ) of ζ 1 , ζ 2 , ... , ζ k and their associated approximation constants. As an application, explicit construction of real numbers ζ 1 , ζ 2 , ... , ζ k with prescribed approximation properties are deduced and illustrated by Matlab plots.

Some solved and unsolved problems in combinatorial number theory, ii

P. Erdős, A. Sárközy (1993)

Colloquium Mathematicae

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In an earlier paper [9], the authors discussed some solved and unsolved problems in combinatorial number theory. First we will give an update of some of these problems. In the remaining part of this paper we will discuss some further problems of the two authors.