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1
Content available remote

On the multiples of a badly approximable vector

100%
Bugeaud Y.
Acta Arithmetica
|
2015
|
tom 168
|
nr 1
71-81
EN
Let d be a positive integer and α a real algebraic number of degree d + 1. Set $α̲:= (α,α²,...,α^{d})$. It is well-known that $c(α̲) := lim inf_{q→ ∞} q^{1/d}·||qα̲|| > 0$, where ||·|| denotes the distance to the nearest integer. Furthermore, $c(α̲)n^{-1/d} ≤ c(nα̲) ≤ nc(α̲)$ for any integer n ≥ 1. Our main result asserts that there exists a real number C, depending only on α, such that $c(nα̲) ≤ Cn^{-1/d}$ for any integer n ≥ 1.
2
Content available remote

On the diophantine equation $x^2 - p^m = ±y^n$

100%
Bugeaud Y.
Acta Arithmetica
|
1997
|
tom 80
|
nr 3
213-223
3
Content available remote

On the greatest prime factor of (ab + 1)(bc + 1)(ca + 1)

100%
Bugeaud Y.
Acta Arithmetica
|
1998
|
tom 86
|
nr 1
45-49
4
Content available remote

Mahler's classification of numbers compared with Koksma's

100%
Bugeaud Y.
Acta Arithmetica
|
2003
|
tom 110
|
nr 1
89-105
5
Content available remote

Linear mod one transformations and the distribution of fractional parts {ξ(p/q)ⁿ}

100%
Bugeaud Y.
Acta Arithmetica
|
2004
|
tom 114
|
nr 4
301-311
6
Content available remote

On a mixed problem in Diophantine approximation

64%
Bugeaud Y., de Mathan B.
Acta Arithmetica
|
2009
|
tom 139
|
nr 1
65-77
7
Content available remote

On simultaneous inhomogeneous Diophantine approximation

64%
Bugeaud Y., Chevallier N.
Acta Arithmetica
|
2006
|
tom 123
|
nr 2
97-123
8
Content available remote

Sets of exact approximation order by rational numbers III

64%
Bugeaud Y., Moreira C.
Acta Arithmetica
|
2011
|
tom 146
|
nr 2
177-193
9
Content available remote

Approximation d'un nombre réel par des nombres algébriques de degré donné

64%
Bugeaud Y., Teulié O.
Acta Arithmetica
|
2000
|
tom 93
|
nr 1
77-86
10
Content available remote

Calcul de la dynamique de transformations linéaires contractantes mod 1 et arbre de Farey

64%
Bugeaud Y., Conze J.-P.
Acta Arithmetica
|
1999
|
tom 88
|
nr 3
201-218
11
Content available remote

Effective results for restricted rational approximation to quadratic irrationals

64%
Bennett M., Bugeaud Y.
Acta Arithmetica
|
2012
|
tom 155
|
nr 3
259-269
12
Content available remote

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

64%
Bugeaud Y., Győry K.
Acta Arithmetica
|
1996
|
tom 74
|
nr 3
273-292
13
Content available remote

On two notions of complexity of algebraic numbers

64%
Bugeaud Y., Evertse J.-H.
Acta Arithmetica
|
2008
|
tom 133
|
nr 3
221-250
14
Content available remote

A quantitative lower bound for the greatest prime factor of (ab+1)(bc+1)(ca+1)

64%
Bugeaud Y., Luca F.
Acta Arithmetica
|
2004
|
tom 114
|
nr 3
275-294
15
Content available remote

Root separation for reducible integer polynomials

64%
Bugeaud Y., Dujella A.
Acta Arithmetica
|
2014
|
tom 162
|
nr 4
393-403
EN
We construct parametric families of (monic) reducible polynomials having two roots very close to each other.
16
Content available remote

Bounds for the solutions of unit equations

64%
Bugeaud Y., Győry K.
Acta Arithmetica
|
1996
|
tom 74
|
nr 1
67-80
17
Content available remote

Morphic and automatic words: maximal blocks and Diophantine approximation

52%
Bugeaud Y., Krieger D., Shallit J.
Acta Arithmetica
|
2011
|
tom 149
|
nr 2
181-199
18
Content available remote

On a mixed Littlewood conjecture in Diophantine approximation

52%
Bugeaud Y., Drmota M., de Mathan B.
Acta Arithmetica
|
2007
|
tom 128
|
nr 2
107-124
19
Content available remote

On the values of a class of analytic functions at algebraic points

52%
Adamczewski B., Bugeaud Y., Luca F.
Acta Arithmetica
|
2008
|
tom 135
|
nr 1
1-18
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