Results 11 to 20 of about 102 (92)
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 $H(\mathbf r)$. Here $H(\mathbf r)$ is the so-called "standard height" of the rational point $\mathbf r$. In this paper
Fishman L, Simmons D.
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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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Simultaneous diophantine approximations and cubic irrationals [PDF]
Pacific Journal of Mathematics, 1969 exaly +4 more sources
RESTRICTED SIMULTANEOUS DIOPHANTINE APPROXIMATION [PDF]
Mathematika, 2016 We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.
Baier, Stephan, Ghosh, Anish
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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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SIMULTANEOUS DIOPHANTINE APPROXIMATION ON POLYNOMIAL CURVES [PDF]
Mathematika, 2009 Let \(\psi: {\mathbb N} \rightarrow {\mathbb R}_+\) be a decreasing function tending to zero. A vector \(x \in {\mathbb R}^n\) is said to be simultaneously \(\psi\)-approximable if the inequality \[ | q x -p | < \psi(| q |) \] has infinitely many solutions \(q \in {\mathbb Z}\), \(p \in {\mathbb Z}^n\).
Budarina, Natalia +2 more
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New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method
Cryptography, 2018 This paper presents new short decryption exponent attacks on RSA, which successfully leads to the factorization of RSA modulus N = p q in polynomial time. The paper has two parts.
Muhammad Rezal Kamel Ariffin +3 more
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Simultaneous Diophantine approximation
Duke Mathematical Journal, 1946 The simplest problems of Diophantine approximation relate to the approximation of a single irrational number 0 by rational numbers pjq, and the principal question is how small we can make the error 0 — pjq in relation to q for infinitely many approximations. It is well known that this question can be answered almost completely in terms of the continued
Davenport, H., Mahler, K.
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ON THE LITTLEWOOD CONJECTURE IN SIMULTANEOUS DIOPHANTINE APPROXIMATION [PDF]
Journal of the London Mathematical Society, 2006 For any given real number $α$ with bounded partial quotients, we construct explicitly continuum many real numbers $β$ with bounded partial quotients for which the pair $(α, β)$ satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.
Adamczewski, Boris, Bugeaud, Yann
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Simultaneous diophantine approximation [PDF]
Bulletin of the Australian Mathematical Society, 1972 AbstractUsing a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394.
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