Page 1

Displaying 1 – 14 of 14

Showing per page

Automatic continued fractions are transcendental or quadratic

Yann Bugeaud (2013)

Annales scientifiques de l'École Normale Supérieure

We establish new combinatorial transcendence criteria for continued fraction expansions. Let  α = [ 0 ; a 1 , a 2 , ... ] be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients ( a ) 1 of  α is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton.

On the exponential local-global principle

Boris Bartolome, Yuri Bilu, Florian Luca (2013)

Acta Arithmetica

Skolem conjectured that the "power sum" A(n) = λ₁α₁ⁿ + ⋯ + λₘαₘⁿ satisfies a certain local-global principle. We prove this conjecture in the case when the multiplicative group generated by α₁,...,αₘ is of rank 1.

Quantitative versions of the Subspace Theorem and applications

Yann Bugeaud (2011)

Journal de Théorie des Nombres de Bordeaux

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.

Currently displaying 1 – 14 of 14

Page 1