Results 11 to 20 of about 158,055 (244)
Approximation to real numbers by cubic algebraic integers. II [PDF]
Annals of Mathematics, 2003 In 1969, H. Davenport and W. M. Schmidt studied the problem of approximation to a real number by algebraic integers of degree at most three. They did so, using geometry of numbers, by resorting to the dual problem of finding simultaneous approximations to and ^2 by rational numbers with the same denominator.
Damien Roy
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Explicit Lower Bounds for Rational Approximation to Algebraic Numbers [PDF]
Proceedings of the London Mathematical Society, 1997 The author gives irrationality measures for some algebraic numbers of degree at least 4. A typical example is \(|{\root 4 \of{5}} -p/q |> 0.03 q^{-2.77}\) for \(p\), \(q\in \mathbb{N}\). This is obtained by using Padé approximation of the binomial function \((1+ x)^\alpha\), with a careful study of the divisibility properties of the coefficients of the
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Simultaneous approximation to algebraic numbers by elements of a number field
Monatshefte f�r Mathematik, 1975 A special case of the main result is as follows. Given a number fieldK a number ɛ>0 and real or complex algebraic numbers ξ1,...,ξn with 1, ξ1,...,ξn linearly independent overK, there are only finitely many α=(α1,...,αn) with components inK and with |ξ1,...,α1| whereH(α) is a suitably defined height.
Wolfgang M Schmidt
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Approximation to real numbers by algebraic integers [PDF]
Acta Arithmetica, 1969 Davenport, Harold, Schmidt, Wolfgang M.
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On the Number of Good Rational Approximations to Algebraic Numbers [PDF]
Proceedings of the American Mathematical Society, 1989 We study rational approximations x / y x/y to algebraic and, more generally, to real numbers ξ \xi . Given δ > 0 \delta > 0 , and writing L = log ( 1 + δ ) L
Mueller, Julia, Schmidt, W. M.
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Describability via ubiquity and eutaxy in Diophantine approximation [PDF]
, 2015 We present a comprehensive framework for the study of the size and large intersection properties of sets of limsup type that arise naturally in Diophantine approximation and multifractal analysis.
Durand, Arnaud
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Simultaneous approximations to p-adic numbers and algebraic dependence via multidimensional continued fractions [PDF]
The Ramanujan Journal, 2021 AbstractUnlike the real case, there are not many studies and general techniques for providing simultaneous approximations in the field of p-adic numbers $$\mathbb Q_p$$ Q p . Here, we study the use of multidimensional continued fractions (MCFs) in this context.
Murru, Nadir, Terracini, Lea
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Karpatsʹkì Matematičnì Publìkacìï, 2019 Algebraic and recursion equations are widely used in different areas of mathematics, so various objects and methods of research that are associated with them are very important.
I.I. Lishchynsky
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Diophantine approximation and deformation [PDF]
, 1999 We associate certain curves over function fields to given algebraic power series and show that bounds on the rank of Kodaira-Spencer map of this curves imply bounds on the exponents of the power series, with more generic curves giving lower exponents. If
Kim, Minhyong +2 more
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On non-conservative perturbations of three-dimensional integrable systems [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамикаAt present, non-conservative perturbations of two-dimensional nonlinear Hamiltonian systems have been studied quite fully. The purpose of the study is to generalize this theory to the three-dimensional case, when the unperturbed system is nonlinear ...
Morozov, Kirill Евгеньевич
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