Results 61 to 70 of about 102 (92)

Simultaneous asymptotic Diophantine approximations

Mathematika, 1967
Let θ 1 , …, θ k be k real numbers. Suppose ψ( t ) is a positive decreasing function of the positive variable t . Define λ( N ), for all positive integers N , to be the number of solutions in integers p 1 …, p k , q of the inequalities ...
William W Adams
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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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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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On Simultaneous Diophantine Approximations

Proceedings of the London Mathematical Society, 1946
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On Optimal Systems and on the Structure of Simultaneous Diophantine Approximations

Analysis (Germany), 1981
W B Jurkat, W Kratz
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Simultaneous Diophantine Approximation

Canadian Journal of Mathematics, 1950
Summary of results. The principal result of this paper is as follows: given any set of real numbers z1, z2, & , zn and an integer t we can find an integer and a set of integers p1, p2 & , pn such that(0.11).Also, if n = 2, we can, given t, produce numbers z1 and z2 such that(0.12)This supersedes the results of Nils Pipping (Acta Aboensis, vol.
openaire   +3 more sources

The Signatures of the Errors of Simultaneous Diophantine Approximations

Proceedings of the London Mathematical Society, 1950
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