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Hausdorff dimension, lower order and Khintchine's theorem in metric Diophantine approximation.
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Khintchine's theorem and its extensions are fundamental in the theory of metric Diophantine approximation as discussed by the authors, and they relate the size of the set of φ-approximable points (defined in (2) below) to a property of the function ψ.Abstract:
Khintchine's theorem and its extensions are fundamental in the theory of metric Diophantine approximation. The theorems relate the size of the set of φ-approximable points (defined in (2) below) to a property of the function ψ. For example, in its onedimensional form, Khintchine's theorem asserts that if the function φ : N -» ί? + is decreasing, then either almost all or almost no real numbers χ satisfyread more
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Metric Diophantine approximation: The Khintchine--Groshev theorem for non-degenerate manifolds
TL;DR: The main objective of as discussed by the authors is to prove a Khintchine type theorem on divergence of linear Diophantine approximation on non-degenerate manifolds, which completes earlier results for convergence.
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On Exponents of Homogeneous and Inhomogeneous Diophantine Approximation
Yann Bugeaud,M. Laurent +1 more
TL;DR: In this paper, it was shown that the inhomogeneous exponent of approximation to a generic point in R by a system of n linear forms is equal to the inverse of the uniform homogeneous exponent associated to the system of dual linear forms.
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Extremal subspaces and their submanifolds
TL;DR: In this paper, it was proved that the properties of almost all points of a smooth submanifold being not very well (multiplicatively) approximable are inherited by nondegenerate points in a smooth smooth sub manifold.
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An extension of quantitative nondivergence and applications to Diophantine exponents
TL;DR: In this article, a sharpening of nondivergence estimates for unipotent (or more gener- ally polynomial-like) flows on homogeneous spaces is presented, which yields precise formulas for Diophantine exponents of affine subspaces of R n and their nondegenerate submanifolds.
Posted Content
Extremal subspaces and their submanifolds
TL;DR: In this article, it was shown that the properties of R^n being not very well (multiplicatively) approximable are inherited by non-degenerate submanifolds, which are not contained in a proper affine subspace.
References
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On the characteristic of functions meromorphic in the unit disk and of their integrals
TL;DR: In this paper, the Nevanlinna characteristic function of a regular function is defined as a convex increasing function with bounded characteristic in the sense that it always exists as a finite or infinite limit.