Results 1 to 10 of about 3,571 (122)
Unconventional height functions in simultaneous Diophantine approximation. [PDF]
Mon Hefte Math, 2017 Simultaneous Diophantine approximation is concerned with the approximation of a point $\mathbf x\in\mathbb R^d$ by points $\mathbf r\in\mathbb Q^d$, with a view towards jointly minimizing the quantities $\|\mathbf x - \mathbf r\|$ and $H(\mathbf r ...
Fishman L, Simmons D.
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Restricted simultaneous Diophantine approximation [PDF]
Mathematika, 2016 We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.Comment: 16 pages.
Baier, Stephan, Ghosh, Anish
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IET Information Security, 2021 A simultaneous Diophantine approximation (SDA) algorithm takes instances of the partial approximate common divisor (PACD) problem as input and outputs a solution.
Wonhee Cho, Jiseung Kim, Changmin Lee
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Successive Minima and Best Simultaneous Diophantine Approximations [PDF]
Monatshefte für Mathematik, 2005 We study the problem of best approximations of a vector $\alpha\in{\mathbb R}^n$ by rational vectors of a lattice $\Lambda\subset {\mathbb R}^n$ whose common denominator is bounded.
Aliev, Iskander, Henk, Martin
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On the Littlewood conjecture in simultaneous Diophantine approximation [PDF]
Journal of the London Mathematical Society, 2005 For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum many real numbers $\beta$ with bounded partial quotients for which the pair $(\alpha, \beta)$ satisfies a strong form of the Littlewood conjecture.
Adamczewski, Boris, Bugeaud, Yann
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Simultaneous p-adic Diophantine approximation [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2023 AbstractThe aim of this paper is to develop the theory of weighted Diophantine approximation of rational numbers to p-adic numbers. Firstly, we establish complete analogues of Khintchine’s theorem, the Duffin–Schaeffer theorem and the Jarník–Besicovitch theorem for ‘weighted’ simultaneous Diophantine approximation in the p-adic case.
Beresnevich, Victor +2 more
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Mathematics, 2021 The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a lattice self ...
Michel L. Lapidus +2 more
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Mathematics, 2021 The modulus of type N=p2q is often used in many variants of factoring-based cryptosystems due to its ability to fasten the decryption process. Faster decryption is suitable for securing small devices in the Internet of Things (IoT) environment or ...
Muhammad Asyraf Asbullah +3 more
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Witnessing a Poincaré recurrence with Mathematica
Results in Physics, 2017 The often elusive Poincaré recurrence can be witnessed in a completely integrable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple numbers.
J.M. Zhang, Y. Liu
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Best Simultaneous Diophantine Approximations under a Constraint on the Denominator [PDF]
, 2005 We investigate the problem of best simultaneous Diophantine approximation under a constraint on the denominator, as proposed by Jurkat. New lower estimates for optimal approximation constants are given in terms of critical determinants of suitable star ...
Aliev, Iskander, Gruber, Peter
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