31 citations · 241 across the 73 of their papers we have counts for
4 papers · 1 filter
Automatic continued fractions are transcendental or quadratic
Yann Bugeaud
We establish new combinatorial transcendence criteria for continued fraction expansions. Let be an algebraic number of degree at least three. One of our crit…
On fractional parts of powers of real numbers close to 1
Yann Bugeaud, Nikolay Moshchevitin
We prove that there exist arbitrarily small positive real numbers such that every integral power $(1 + \vepsilon)^n$ is at a distance greater than $2^{-17} ε|\log \vepsilon|^{-…
Transcendence with Rosen continued fractions
Yann Bugeaud, Pascal Hubert, Thomas A. Schmidt
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 num…
Root separation for irreducible integer polynomials
Yann Bugeaud, Andrej Dujella
We establish new results on root separation of integer, irreducible polynomials of degree at least four. These improve earlier bounds of Bugeaud and Mignotte (for even degree) and…