[PDF] Top 20 Metric Diophantine Approximation : aspects of recent work
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Metric Diophantine Approximation : aspects of recent work
... In [14], a general framework is developed for establishing divergent results analogous to those of Khintchine and Jarn´ık for a natural class of lim sup sets. The framework is based on the notion of ‘ubiquity’, which ... See full document
84
Non-planarity and metric Diophantine approximation for systems of linear forms
... consider inhomogeneous versions of extremality in the standard, weighted and multiplica- tive settings (see §6 for precise definitions). In this paper we establish that within all the three settings inhomogeneous and ... See full document
30
Sums of reciprocals of fractional parts and multiplicative Diophantine approximation
... The existence of a single pair (α, β) satisfying (2.14) was conjectured by Cassels in the 1950s and remained open until the recent work of Shapira [51]. He showed the validity of (2.14) for almost all pairs ... See full document
102
Diophantine Approximation and applications in Interference Alignment
... a recent series of publications, including [11,12, 14–17,21–23], which utilise the theory of metric Diophantine approximation to develop new approaches in interference alignment, a concept ... See full document
50
Metrical Diophantine approximation for quaternions
... Approximating complex numbers by ratios of Gaussian integers Z[i], a half way house to approximating quaternions by ratios of Lipschitz or Hurwitz integer quaternions, was studied by Hermite and Hurwitz in the 19th ... See full document
31
On Diophantine transference principles
... of Diophantine approximation on manifolds discussed so far can be generalized to the context of smooth submanifolds of matrices, ...for recent devel- opments on this ...phantine approximation ... See full document
22
Diophantine approximation and coloring
... the approximation of real numbers by ...of approximation of real numbers can be phrased as problems about the orbits of points in certain spaces ...compact metric spaces) under the action of ... See full document
17
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces
... of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric ...more recent results of Hersonsky and Paulin (’02, ’04, ...prior work of which we are ... See full document
100
Intrinsic Diophantine approximation on manifolds : General theory
... to Diophantine approximation can be asked in a much broader ...complete metric space (X, dist), a countable subset Q ⊆ X and a height function H : Q → (0, ...a Diophantine triple, and denote ... See full document
18
A note on three problems in metric Diophantine approximation
... of Diophantine approximation on manifolds ...of Diophantine approximation on manifolds has developed at some considerable pace with the catalyst being the pioneering work of Kleinbock ... See full document
23
Higher rank Bohr sets and multiplicative diophantine approximation
... Abstract. Gallagher’s theorem is a sharpening and extension of the Lit- tlewood conjecture that holds for almost all tuples of real numbers. We provide a fibre refinement, solving a problem posed by Beresnevich, Haynes ... See full document
22
Diophantine approximation on manifolds and lower bounds for Hausdorff dimension
... First some notation. Throughout, R k will be regarded as a metric space with distance induced by any fixed norm (not necessarily Euclidean) and B (x, r) will denote a ball centred at x ∈ R k of radius r > 0. ... See full document
21
An approach to the approximation of common coupled fixed points of contractive maps in metric-type spaces
... In this work, we provide a novel technique of tackling coupled fixed point inequalities of type (1.5), which also works for inequalities of type (1.4), without the use of the classical concept of Cauchy sequences. ... See full document
19
Unconventional height functions in simultaneous Diophantine approximation
... where lcm : N d → N is the least common multiple function. Historically, this height function and its variations and generalizations (see e.g. [6, §VIII.5-6]) have played a major role in modern mathematics, not only in ... See full document
30
Unconventional height functions in simultaneous Diophantine approximation
... The main technique of this paper is to generalize the correspondence between the continued fraction expansion of an irrational number and its Diophantine properties into higher dimensions. This is done by ... See full document
43
Badly approximable points on manifolds
... natural Diophantine condition. The most recent results established in [3] by An, Velani and the author of this paper remove condition (5) from the findings of [17] and at the same time settle Davenport’s ... See full document
43
Daneš theorem in complete random normed modules
... A random normed module is a random generalization of an ordinary normed space. Different from ordinary normed spaces, random normed modules possess the rich strat- ification structure, which is introduced in this paper. It ... See full document
6
Badly approximable points in twisted Diophantine approximation and Hausdorff dimension
... best approximation vectors (see also ...best approximation vectors are discussed in [19,20] and a recent survey on the topic is due to Chevallier ... See full document
17
Badly approximable points in twisted Diophantine approximation and Hausdorff dimension
... Best approximation vectors have been introduced since a long time inside proofs in an unexplicit ...A recent survey on the topic is due to Chevallier ...best approximation vectors are discussed in ... See full document
18
Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
... intrinsic Diophantine approximation is concerned with finding rational approximations to an irrational number x ∈ F by rational numbers that lie on the fractal ...intrinsic approximation on the Cantor ... See full document
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