Results 11 to 20 of about 1,648,333 (245)
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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Sugaku Expositions, 2021 This article gives an introductory survey of recent progress on Diophantine problems, especially consequences coming from Schmidt’s subspace theorem, Baker’s transcendence method and Padé approximation.
N. Hirata-Kohno
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On Inhomogeneous Diophantine Approximation [PDF]
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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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, Qing-Shan 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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Diophantine approximation in metric space [PDF]
, 2021 Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a ...
Fraser, Jonathan M. +2 more
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Inhomogeneous diophantine approximation for generic homogeneous functions [PDF]
International Journal of Number Theory, 2022 The present paper is a sequel to [Monatsh.~Math.\ {\bf 194} (2021), 523--554] in which results of that paper are generalized so that they hold in the setting of inhomogeneous Diophantine approximation. Given any integers $n \geq 2$ and $\ell \geq 1$, any
Dmitry Kleinbock, Mishel Skenderi
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On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n [PDF]
, 2010 In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers.
Farzaneh , A. +3 more
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