Results 91 to 100 of about 3,571 (122)

On simultaneous diophantine approximation

Rendiconti del Circolo Matematico di Palermo, 1984
For given \(s\in {\mathbb{N}}\), let \(\theta_ s\) denote the supremum of all reals c with the property that, for any vector \({\bar \alpha}=(\alpha_ 1,...,\alpha_ s)\in({\mathbb{R}}^ s-{\mathbb{Q}}^ s),\) there exist infinitely many \((\bar p,q)\in {\mathbb{Z}}^ s\times {\mathbb{N}}\) satisfying \(| {\bar \alpha}-(1/q)\bar p| \leq c^{-1/s}\quad q^{-1 ...
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Simultaneous diophantine approximations and Hermite's method

Bulletin of the Australian Mathematical Society, 1980
In this paper we generalize a result of Mahler on rational approximations of the exponential function at rational points by proving the following theorem: letnε N* and αl, …, αnbe distinct non-zero rational numbers; there exists a constantc=c(n, αl, …, αn) ≥ 0 such thatfor every non-zero integer point (qo,ql, …,qn)andq= max {|ql|, … |qn|, 3}.
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On simultaneous diophantine approximations. Vectors of given diophantine type

Mathematical Notes, 1997
Let \(\psi(y)\) be a real-valued function of a real argument. A positive integer \(p\) is called a simultaneous \(\psi\)-approximation for the numbers \(\alpha_1,\dots,\alpha_s\in \mathbb R\) if \[ \max_{1\leq j\leq s}\| p\alpha_j\|\leq \psi(p)\;(\text{here }\|\alpha\|= \min_{z\in \mathbb Z}| \alpha- z|). \] The numbers \(\alpha_1,\dots, \alpha_s\) are
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ON THE SIMULTANEOUS DIOPHANTINE APPROXIMATION OF NEW PRODUCTS

Analysis, 2000
Let \(K\) denote \(\mathbb Q\) or \({\mathbb Q}(i)\) and let \(O_K\) be the ring of integers of \(K\). Let \(q\) be an element of \(O_K\) with \(|q|>1\) and let \(a\) and \(\alpha\) be non-zero elemts of \(K\) such that \(\pm\alpha, -a\alpha\neq q^j\) for any positive integer \(j\). Let \[ f(z)=\prod_{j=1}^\infty g(zq^{-j}) \] where \(g(z)=\left(1+az-z^
Bundschuh, Peter, Väänänen, Keijo
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Simultaneous diophantine approximations with nonmonotonic error function

Doklady Mathematics, 2011
The paper under review contains the announcement of two results along with sketches of their proofs. Both are concerned with algebraic approximation. The first result concerns the inequality \[ | P(x) +d | < \psi(H(P)), \] where \(d\) is a fixed real number, \(P\) varies over the integer polynomials of degree at most \(n \geq 2\) and \(H(P)\) denotes ...
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Hausdorff Dimension and Generalized Simultaneous Diophantine Approximation

Bulletin of the London Mathematical Society, 1998
Suppose that \(m\) is a positive integer, \(\underline{\tau}=(\tau_1,\dots,\tau_m)\) is a vector of positive real numbers, and \(Q\) is an infinite set of positive integers. Let \(W_Q(m;\underline{\tau})\) be the set of points \(\mathbf x=(x_1,\dots,x_m)\in \mathbb R^m\) for which the inequalities \(\|x_iq\|
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The computational complexity of simultaneous Diophantine approximation problems

23rd Annual Symposium on Foundations of Computer Science (sfcs 1982), 1982
Let \(a=(a_ 1/b_ 1,...,a_ d/b_ d)\) be a rational vector. An integer q is called a best simultaneous diophantine approximation denominator (BSAD) of a if \(\{\) \(\{\) qa\(\}\) \(\}\leq \{\{q'a\}\}\) for all q'\(\in [1,q]\), where \(\{\{qa\}\}=\max (\{q_ ia_ i/b_ i\})\) is the distance to a nearest integer vector.
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On simultaneous Diophantine approximation

Monatshefte für Mathematik, 2022
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Simultaneous Diophantine Approximation

Journal of the London Mathematical Society, 1955
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Simultaneous Diophantine Approximation (II)†

Proceedings of the London Mathematical Society, 1955
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