Results 11 to 20 of about 2,483 (259)
Diophantine Approximation and Coloring [PDF]
The American Mathematical Monthly, 2015 16 pages, pre-publication version of paper which will appear in American Mathematical ...
Alan Haynes, Sara Munday
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A note on Diophantine approximation
International Journal of Mathematics and Mathematical Sciences, 2005 We prove the existence of a dense subset Δ of [0, 4] such that for all α ∈ Δ there exists a subgroup Xα of infinite rank of ℤ[z] such that Xα is a discrete subgroup of C[0, β] for all β ≥ α but it is not a discrete subgroup of C[0, β] for any β ∈ (0, α).Given a set of nonnegative real numbers , a Λ‐polynomial (or Müntz polynomial) is a function of the
J. M. Almira +2 more
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On Diophantine approximation by unlike powers of primes
Open Mathematics, 2019 Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irrational, λ2/λ4 and λ3/λ5 are rational. Let η real, and ε > 0.
Ge Wenxu, Li Weiping, Wang Tianze
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On Inhomogeneous Diophantine Approximation
Journal of Number Theory, 1994 Let \(\alpha\) and \(\beta\) be irrational numbers, \(\beta\) not of the form \(m\alpha+ n\) (\(m\), \(n\) integers) and define \[ M(\alpha, \beta)= \liminf \{| q|\;\| q\alpha- \beta\|:\;| q|\to \infty\} \] to be the inhomogeneous approximation constant for the pair \(\alpha\), \(\beta\).
Cusick, T.W., Rockett, A.M., Szusz, P.
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Remarks on Diophantine approximation in function fields [PDF]
Mathematica Scandinavica, 2018 We study some problems in metric Diophantine approximation over local fields of positive characteristic.
Arijit Ganguly, Anish Ghosh
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Multiplicative p-adic metric Diophantine approximation on manifolds and dichotomy of exponents [PDF]
Bulletin de la Société Mathématique de France, 2019 In this paper we study $p$-adic Diophantine approximation on manifolds, specifically multiplicative Diophantine approximation on affine subspaces and a Diophantine dichotomy for analytic $p$-adic manifolds.
Shreyasi Datta, Anish Ghosh
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AN OPTIMAL BOUND FOR THE RATIO BETWEEN ORDINARY AND UNIFORM EXPONENTS OF DIOPHANTINE APPROXIMATION [PDF]
Mathematika, 2018 We provide a lower bound for the ratio between the ordinary and uniform exponent of both simultaneous Diophantine approximation and Diophantine approximation by linear forms in any dimension.
Antoine Marnat, N. Moshchevitin
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Diophantine Approximation and Dirichlet Series
Texts and Readings in Mathematics, 2020 The second edition of the book includes a new chapter on the study of composition operators on the Hardy space and their complete characterization by Gordon and Hedenmalm. The book is devoted to Diophantine approximation, the analytic theory of Dirichlet
H. Queffélec, M. Queffélec
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Uniform Diophantine approximation and run-length function in continued fractions [PDF]
Ergodic Theory and Dynamical Systems, 2023 We study the multifractal properties of the uniform approximation exponent and asymptotic approximation exponent in continued fractions. As a corollary, we calculate the Hausdorff dimension of the uniform Diophantine set $$ \begin{align*} {\mathcal{U ...
Bo Tan, Qingshan Zhou
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Quantitative inhomogeneous Diophantine approximation for systems of linear forms [PDF]
Proceedings of the American Mathematical Society, 2023 The inhomogeneous Khintchine–Groshev Theorem is a classical generalization of Khintchine’s Theorem in Diophantine approximation, by approximating points in R m \mathbb {R}^m by systems of linear forms ...
Manuel Hauke
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