Results 81 to 90 of about 3,571 (122)

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.
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Metric Simultaneous Diophantine Approximation

Journal of the London Mathematical Society, 1962
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Simultaneous Diophantine Approximation Using Primes

Bulletin of the London Mathematical Society, 1988
The authors consider k-tuples of reals \((\alpha_ 1,...,\alpha_ k)\) which satisfy the compatibility condition: If \(h_ i\in {\mathbb{Z}}\) for \(1\leq i\leq k\) and \(\sum^{k}_{i=1}h_ i\alpha_ i\in {\mathbb{Q}}\) then \(\sum^{k}_{i=1}h_ i\alpha_ i\in {\mathbb{Z}}\).
Balog, A., Friedlander, J.
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Simultaneous Diophantine Approximation

Proceedings of the London Mathematical Society, 1952
Proof of the theorem: ``Let \(c > 46^{-1/4}\). Then, for every pair of real irrational numbers \(\alpha, \beta\), there exist infinitely many solutions \(p, q, r > 0\) of \(r(p-\alpha r)^2 < c\), \(r(q- \beta r)^2 < c\) in integers.'' This result slightly improves one by \textit{P. Mullender} [Ann. Math. (2) 52, 417-426 (1950; Zbl 0037.17102)].
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SIMULTANEOUS DYNAMICAL DIOPHANTINE APPROXIMATION IN BETA EXPANSIONS

Bulletin of the Australian Mathematical Society, 2020
Let $\unicode[STIX]{x1D6FD}>1$ be a real number and define the $\unicode[STIX]{x1D6FD}$-transformation on $[0,1]$ by $T_{\unicode[STIX]{x1D6FD}}:x\mapsto \unicode[STIX]{x1D6FD}x\hspace{0.6em}({\rm mod}\hspace{0.2em}1)$. Let $f:[0,1]\rightarrow [0,1]$ and $g:[0,1]\rightarrow [0,1]$ be two Lipschitz functions.
WEILIANG WANG, LU LI
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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 ...
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Simultaneous Diophantine Approximation To Series

Journal of the London Mathematical Society, 1959
Es sei \(\mathfrak K\) die Menge aller formalen Laurentreihen \(x = \alpha_d z^d + \alpha_{d-1}z^{d-1}+ \ldots\) mit Koeffizienten aus einem Körper \(\mathfrak k\). Es werde ferner \(\mathfrak T = \mathfrak k [z]\) und \(\mathfrak R = \mathfrak k(z)\) gesetzt.
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