metric diophantine approximation
Non-planarity and metric Diophantine approximation for systems of linear forms
... Basic examples of good and nonplanar pairs (f , µ) are given by µ = λ (Lebesgue measure on R d ) and f smooth and nondegenerate, see [27, Proposition 3.4]. The paper [26] introduces a class of friendly measures: a ...
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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 ...
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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 & ...
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A zero-infinity law for well-approximable points in Julia sets
... classical set W (τ ) := { x ∈ R : | x − p/q | ≤ q − τ for infinitely many rationals p/q } of well approximable numbers. For Julia sets associated with rational maps, we proved [4] the following analogue of the ...
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Diophantine approximation in Kleinian groups : singular, extremal, and bad limit points
... Without assuming that G is of the first kind, Theorem KT is essentially established in [38] if y is a hyperbolic fixed point of G and in [40] if y is a parabolic fixed point of G. We say essentially, since in both [38] ...
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Diophantine Approximation and applications in Interference Alignment
... of metric Diophantine approximation to develop new approaches in interference alignment, a concept within the field of wireless com- munication ...in Diophantine ap- proximation which crop up, ...
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Diophantine approximation on manifolds and lower bounds for Hausdorff dimension
... This statement is a natural generalisation of Khintchine’s theorem (a Lebesgue measure statement) to Hausdorff measures and it is easily verified that it im- plies (1.3). It is worth pointing out that there is an even ...
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Inhomogeneous dual Diophantine approximation on affine subspaces
... of Diophantine approximation on man- ifolds, specifically inhomogeneous approximation on affine ...of metric Diophantine approximation on manifolds studies the conditions under ...
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Diophantine approximation in Kleinian groups : singular, extremal, and bad limit points
... Without assuming that G is of the first kind, Theorem KT is essentially established in [37] if y is a hyperbolic fixed point of G and in [39] if y is a parabolic fixed point of G. We say essentially, since in both [37, 39] ...
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Inhomogeneous theory of dual Diophantine approximation on manifolds
... inhomogeneous Diophantine approximation on manifolds is ...as Diophantine approximation by algebraic integers. Keywords: Metric Diophantine approximation, extremal ...
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Higher rank Bohr sets and multiplicative diophantine approximation
... 1.6. Funding and acknowledgments. The authors were supported by EP- SRC Programme Grant EP/J018260/1. SC was also supported by EPSRC Fellowship Grant EP/S00226X/1. We thank Victor Beresnevich, Lifan Guan, Mumtaz Hussain, ...
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Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces
... of Diophantine approximation are Dirichlet’s theorem on the ap- proximability of every point with respect to the function 1/q 2 (supplemented by Liouville’s result regarding the optimality of this ...
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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 ...
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On Diophantine transference principles
... for all x ∈ M . (1.15) We postpone the proof and discussion about these lower bounds to section 3. Here and later, we provide a lower bound for inhomogeneous exponents in term of their corresponding homogeneous exponent. ...
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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 ...best approximation vectors are discussed in [19, ...
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Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
... Intrinsic Diophantine approximation on fractals, such as the Cantor ternary set, was undoubt- edly motivated by questions asked by ...to Diophantine approximation on certain ...
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Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
... In order to state our main theorem for this section, let us briefly recall the def- inition and basic properties of the Hausdorff dimension of a fractal † F ⊆ R d , see, e.g., [8, Chapters 2-3]. Let d denote the standard ...
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Badly approximable points on manifolds
... tine approximation, namely, Davenport’s problem regarding badly approx- imable points on submanifolds of a Euclidean space and Schmidt’s problem regarding the intersections of the sets of weighted badly ...
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DA-Encrypt: Homomorphic Encryption via Non-Archimedean Diophantine Approximation --- Preliminary Report
... In this paper, we present a theoretical description of a new sym- metric somewhat homomorphic encryption scheme inspired by ideas from the theory of (non-archimedean) Diophantine approximation. We ...
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ON A CLASS OF SOLUTIONS FOR THE HYPERBOLIC DIOPHANTINE EQUATION
... the polynomial P has integral coefficients and one is interested in solutions for which all the unknowns take integer values. Diophantine equations are rich in variety. Two-variable Diophantine equation ...
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