Results 11 to 20 of about 3,571 (122)
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.
openaire +2 more sources
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
openaire +3 more sources
On Approximation constants for Liouville numbers [PDF]
, 2015 We investigate some Diophantine approximation constants related to the simultaneous approximation of $(\zeta,\zeta^{2},\ldots,\zeta^{k})$ for Liouville numbers $\zeta$. For a certain class of Liouville numbers including the famous representative $\sum_{n\
Jarník +7 more
core +3 more sources
PKCHD: Towards a Probabilistic Knapsack Public-Key Cryptosystem with High Density
Information, 2019 By introducing an easy knapsack-type problem, a probabilistic knapsack-type public key cryptosystem (PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy knapsack sequence. Thence, to recover the trapdoor information, the implicit
Yuan Ping +4 more
doaj +1 more source
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.
openaire +3 more sources
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
doaj +1 more source
Simultaneous inhomogeneous diophantine approximation on manifolds [PDF]
Journal of Mathematical Sciences, 2012 Dedicated to A.O.
Beresnevich, V. V., Velani, S. L.
openaire +3 more sources
Numerical Methods for Quasicrystals [PDF]
, 2013 Quasicrystals are one kind of space-filling structures. The traditional crystalline approximant method utilizes periodic structures to approximate quasicrystals.
Jiang, Kai, Zhang, Pingwen
core +1 more source
Metrical Diophantine approximation for quaternions [PDF]
, 2014 Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup' sets.Comment: 30 pages.
Beresnevich +27 more
core +2 more sources
On simultaneous inhomogeneous Diophantine approximation [PDF]
Acta Arithmetica, 2006 In this paper, the authors study inhomogeneous problems in metrical Diophantine approximation. For a tuple \(\underline{\alpha} = (\alpha_1, \dots, \alpha_k) \in {\mathbb R}^k\) and real numbers \(v,w>0\), let \({\mathcal V}_v(\underline{\alpha})\) denote the set of \(\xi \in {\mathbb R}\) for which there is a \(c > 0\) such that the inequality ...
Bugeaud, Yann, Chevallier, Nicolas
openaire +3 more sources