Results 41 to 50 of about 1,648,333 (245)
Quantitative Diophantine approximation with congruence conditions [PDF]
Journal de Théorie des Nombres de Bordeaux, 2020 In this short paper we prove a quantitative version of the Khintchine-Groshev Theorem with congruence conditions. Our argument relies on a classical argument of Schmidt on counting generic lattice points, which in turn relies on a certain variance bound ...
Mahbub Alam, Anish Ghosh, Shucheng Yu
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Diophantine approximation and deformation [PDF]
Bulletin de la Société mathématique de France, 2000 We associate certain curves over function fields to given algebraic power series and show that bounds on the rank of Kodaira-Spencer map of this curves imply bounds on the exponents of the power series, with more generic curves giving lower exponents.
Kim, M, Thakur, D, Voloch, J
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Diophantine Approximation and Diophantine Equations [PDF]
, 2018 P. Corvaja, U. Zannier
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Metric Diophantine approximation on homogeneous varieties [PDF]
, 2014 We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik theorems. In full generality our results establish simultaneous Diophantine
Nevo, Amos +3 more
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GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS [PDF]
, 2002 This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers ...
Sándor, József
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Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution.
Pierre Arnoux +3 more
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Lower bounds for simultaneous Diophantine approximation constants [PDF]
, 2014 summary:After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants $\theta _s$, new lower bounds are deduced for $\theta _6$ and $\theta _7$
Nowak, Werner Georg
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On Diophantine transference principles [PDF]
, 2018 We provide an extension of the transference results of Beresnevich and Velani connecting homogeneous and inhomogeneous Diophantine approximation on manifolds and provide bounds for inhomogeneous Diophantine exponents of affine subspaces and their ...
ANTOINE MARNAT +3 more
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A Zero-One Law for Uniform Diophantine Approximation in Euclidean Norm [PDF]
International mathematics research notices, 2019 We study a norm-sensitive Diophantine approximation problem arising from the work of Davenport and Schmidt on the improvement of Dirichlet’s theorem. Its supremum norm case was recently considered by the 1st-named author and Wadleigh [ 17], and here we
D. Kleinbock, Anurag Rao
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On applications of diophantine approximations [PDF]
Proceedings of the National Academy of Sciences, 1984 This paper is devoted to the study of the arithmetic properties of values of G -functions introduced by Siegel [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1].
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