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Approximation by Algebraic Numbers

- Y. Bugeaud
- Mathematics
- 8 November 2004

Preface Frequently used notation 1. Approximation by rational numbers 2. Approximation to algebraic numbers 3. The classifications of Mahler and Koksma 4. Mahler's conjecture on S-numbers 5.… Expand

On Exponents of Homogeneous and Inhomogeneous Diophantine Approximation

- Y. Bugeaud, M. Laurent
- Mathematics
- 2005

In Diophantine Approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of… Expand

Exponents of Diophantine Approximation and Sturmian Continued Fractions

- Y. Bugeaud, M. Laurent
- Mathematics
- 3 June 2004

Soient ( un nombre reel et n un entier strictement positif. Nous definissons quatre exposants d'approximation diophantienne, qui viennent completer les exposants ω n (ξ) et ω* n (ξ) definis par… Expand

Bounds for the solutions of Thue-Mahler equations and norm form equations

- Y. Bugeaud, K. Gyory
- Mathematics
- 1996

Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers

- Y. Bugeaud, M. Mignotte, S. Siksek
- Mathematics
- 2 March 2004

This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based… Expand

On the complexity of algebraic numbers I. Expansions in integer bases

- B. Adamczewski, Y. Bugeaud
- Mathematics
- 28 November 2005

Let b ≥ 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are… Expand

On the number of solutions of the generalized Ramanujan-Nagell equation

- Y. Bugeaud, T. N. Shorey
- Mathematics
- 20 January 2001

Let D 1 and D 2 be coprime positive integers and let k be an odd positive integer coprime with D 1 D 2 . We consider the Diophantine equation D 1 x 2 + D 2 = k n in the unknowns x≥1, n≥1. We give a… Expand

On the complexity of algebraic numbers, II. Continued fractions

- B. Adamczewski, Y. Bugeaud
- Mathematics
- 28 November 2005

The continued fraction expansion of an irrational number $\alpha$ is eventually periodic if and only if $\alpha$ is a quadratic irrationality. However, very little is known regarding the size of the… Expand

Diophantine approximation and Cantor sets

- Y. Bugeaud
- Mathematics
- 2 February 2008

We provide an explicit construction of elements of the middle third Cantor set with any prescribed irrationality exponent. This answers a question posed by Kurt Mahler.

A NOTE ON INHOMOGENEOUS DIOPHANTINE APPROXIMATION

- Y. Bugeaud
- MathematicsGlasgow Mathematical Journal
- 1 January 2003

Let $\alpha$ be an irrational number. We determine the Hausdorff dimension of sets of real numbers which are close to infinitely many elements of the sequence $(\{n\alpha\})_{n\,{\ge}\,1}$.

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