On transfer inequalities in Diophantine approximation, II |
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Authors: | Yann Bugeaud Michel Laurent |
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Affiliation: | 1. Université de Strasbourg, U. F. R. de mathématiques, 7, rue René Descartes, 67084, Strasbourg, France 2. Institut de Mathématiques de Luminy, C.N.R.S., U.M.R. 6206, case 907, 163, avenue de Luminy, 13288, Marseille Cedex 9, France
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Abstract: | Let Θ be a point in R n . We are concerned with the approximation to Θ by rational linear subvarieties of dimension d for 0 ≤ d ≤ n−1. To that purpose, we introduce various convex bodies in the Grassmann algebra Λ(R n+1). It turns out that our convex bodies in degree d are the dth compound, in the sense of Mahler, of convex bodies in degree one. A dual formulation is also given. This approach enables us both to split and to refine the classical Khintchine transference principle. |
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