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Lower bound for the normalized height in small codimension
The starting point of this thesis is the study of Lehmer's problem in dimension greater than two. It aims at finding, in the more general context of the multiplicative... -
Spiraling spectra of geodesic lines in negatively curved manifolds
Revised version. Appeared in Math. Z. 268 (2011) 101-142. -
On the closedness of approximation spectra
Paru dans J. Th. Nb. Bordeaux 21 (2009) 701-710. -
On the almost sure spiraling of geodesics in negatively curved manifolds
35 pages, 5 figures, paru dans J. Diff. Geom. 85 (2010) 271-314. -
Some remarks concerning the rank of mapping tori and ascending HNN-extensions...
International audience -
About the Schneider-Lang theorem
The Schneider-Lang theorem is a classic transcendence criterion for complex numbers. It asserts that there are only finitely many points at which algebraically... -
Approximation diophantienne dans les variétés abéliennes
This thesis aims at providing a quantitative version of the following theorem : there are only finitely many approximations with positive exponent of any subvariety of... -
Hardy-Littlewood series and even continued fractions
International audience -
Applications of geometric invariant theory to diophantine geometry
Geometric invariant theory is a central subject in nowadays' algebraic geometry : developed by Mumford in the early sixties, it enhanced the knowledge of projective... -
Some contributions at the study of Laurent series with coefficients in a fini...
This thesis looks at the interplay of three important domains: combinatorics on words, theory of finite-state automata and number theory. More precisely, we show how... -
Sphere Packings and Beta-Integers
Sphere packings, mostly in R^n, and beta-integers, are the objects considered in this thesis. They are indifferently described in the language of sphere packings or in... -
Exponents of Diophantine approximation and Sturmian continued fractions
Let $\xi$ be a real number and let $n$ be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents $w_n(\xi)$ and... -
On simultaneous diophantine approximations to $\zeta(2)$ and $\zeta(3)$
The authors present a hypergeometric construction of rational approximations to $\zeta(2)$ and $\zeta(3)$ which allows one to demonstrate simultaneously the... -
Logarithm laws for equilibrium states in negative curvature
Let $M$ be a pinched negatively curved Riemannian manifold, whose unit tangent bundle is endowed with a Gibbs measure $m_F$ associated to a potential $F$. We compute...
