On transfer inequalities in Diophantine approximation, II
نویسندگان
چکیده
Let Θ be a point in R. 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). It turns out that our convex bodies in degree d are the d-th 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.
منابع مشابه
On Transfer Inequalities in Diophantine Approximation
Let Θ be a point in R. We split the classical Khintchine’s Transference Principle into n − 1 intermediate estimates which connect exponents ωd(Θ) measuring the sharpness of the approximation to Θ by linear rational varieties of dimension d, for 0 ≤ d ≤ n− 1. We also review old and recent results related to these n exponents.
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