Sur le spectre des exposants d'approximation diophantienne classiques et pondérés

Abstract : Given a n-tuple of real numbers, seen as a point in the projective space, one can define for eachindex d between 0 and n-1 two exponents of diophantine approximation (an ordinary and auniform) which measure the approximability of this n-tuple by rational subspaces of dimension d inthe projective space. These 2n exponents are not independant. This thesis is part of the study fromthe spectrum of all or part of these exponents, which have been much studied recently. We userecent tools coming from the parametric geometry of numbers to study the spectrum of the uniformexponents, and deal with a twisted case in dimension two.
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Antoine Marnat. Sur le spectre des exposants d'approximation diophantienne classiques et pondérés. Théorie des nombres [math.NT]. Université de Strasbourg, 2015. Français. ⟨NNT : 2015STRAD042⟩. ⟨tel-01226270v2⟩

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