A Groshev Type Theorem for Convergence on Manifolds

By Victor Beresnevich. 2002

102 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/815f65d1182b3937b1f178e861336c8bf1673f0f

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Real Interference Alignment: Exploiting the Potential of Single Antenna Systems (2009, background): “Theorem 5 ( [24] and [25]): and g 1 , g 2 , . . . , g m be functions from R n to R with the following conditions: 1) g i for i ∈ { 1 , 2 , . . . , . . . , , m is analytic, 2) 1 , g 1 , g 2 g m are linearly independent over R .”
Rational points near manifolds and metric Diophantine approximation (2009, methodology): “1 has been fully settled [3], [6], [19] and very deep answers regarding the dual version of Problem 2.”
Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation (2005, background): “In recent years the case S = {∞} has been completely understood, see [BKM, Be ] for the convergence case and [BBKM] for the divergence case.”
An extension of quantitative nondivergence and applications to Diophantine exponents (2005, background): “ifolds M of Rnare called of Groshev type for convergence (resp. divergence) if the convergence (resp. divergence) of (6.5) implies that almost no (resp. almost all) points of M are in Wψ. It is known [5, 1, 3] that nondegenerate submanifolds M of Rn are of Groshev type for both convergence and diver”
Badly approximable points on manifolds (2013, background): “In the theory of Diophantine approximation on manifolds, see for instance, [7–9,31,33], there are already well established classes of manifolds of interest.”
Interference Alignment: A New Look at Signal Dimensions in a Communication Network (2011, background): “The separability of rational dimensions is a consequence of the (extensions of) Khintchine–Groshev theorem [10, 12] in Diophantine approximation theory.”