Results 11 to 20 of about 788,130 (111)
Simultaneous Diophantine approximation of rationals by rationals [PDF]
Journal of Number Theory, 1986 For positive integers \(n\geq 2\), \(B\geq 2\), let \(S_ n(B)\) denote the set of rational vectors \(\alpha =(a_ 1/B,...,a_ n/B)\) with \(a_ j\in {\mathbb{Z}}\), \(0\leq a_ j0\), define N(\(\alpha\),\(\Delta)\) as the number of vectors \(\zeta =(x_ 1/x,...,x_ n/x)\) with \(1\leq ...
Lagarias, Jeffrey C, Hastad, Johan T
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Best simultaneous diophantine approximations under a constraint on the denominator [PDF]
, 2006 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 ...
Aliev, Iskander, Gruber, Peter M.
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Simultaneous rational approximations and related diophantine equations.
, 1990 We construct algebraic numbers for which especially sharp effective linear independence and simultaneous approximation measures can be proved. Similar results were obtained previously by Osgood and Fel'dman, but in certain special cases our results are ...
Rickert, John Henry
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Diophantine approximations using Padé approximations [PDF]
, 2000 We show how Padé approximations are used to get Diophantine approximations of real or complex numbers, and so to prove the irrationality. We present two kinds of examples.
M. Prévost, Prévost, M.
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GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS [PDF]
, 2002 This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers ...
Sándor, József
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Simultaneous inhomogeneous diophantine approximation on manifolds [PDF]
Journal of Mathematical Sciences, 2012 Dedicated to A.O.
Beresnevich, V. V., Velani, S. L.
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Lower bounds for simultaneous Diophantine approximation constants [PDF]
, 2014 summary:After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants $\theta _s$, new lower bounds are deduced for $\theta _6$ and $\theta _7$
Nowak, Werner Georg
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A note on the quality of simultaneous Diophantine approximations obtained by the LLL algorithm
, 2023 In 1982, A. K. Lenstra, H. W. Lenstra, and L. Lov\'asz introduced the first polynomial-time method to factor a nonzero polynomial $f \in \mathbb{Q}[x]$ into irreducible factors.
van Frankenhuijsen, Machiel +1 more
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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
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On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n [PDF]
, 2010 In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers.
Farzaneh , A. +3 more
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