Results 41 to 50 of about 157,767 (127)
Effective approximation to complex algebraic numbers by algebraic numbers of bounded degree
Transactions of the American Mathematical SocietyWe establish the first effective improvements on the Liouville inequality for approximation to complex non-real algebraic numbers by complex algebraic numbers of degree at most 4 4 .
Bajpai, Prajeet, Bugeaud, Yann
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Physical Sciences and Technology, 2018 To consider the interactions between light nuclei, as well as the nature of the nuclear forces between them, and the test was made of the coupled and resonant positions of the nucleus (_3^6)Li using the technique of the "Algebraic version of the ...
N.K. Kalzhigitov +4 more
doaj
Simultaneous approximation to algebraic numbers by rationals
Acta Mathematica, 1970 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Effective approximation to complex algebraic numbers by quadratic numbers
Canadian Mathematical BulletinAbstractWe establish an effective improvement on the Liouville inequality for approximation to complex nonreal algebraic numbers by quadratic complex algebraic numbers.
Prajeet Bajpai, Yann Bugeaud
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Approximation to certain transcendental decimal fractions by algebraic numbers
Journal of Number Theory, 1991 For a positive integer \(g\geq 2\) consider the number \(M(g)=0.(1)_ g(2)_ g...(n)_ g...\) where for \(n\in {\mathbb{N}}\) \((n)_ g\) means digit representation of n to base g and \(0.(1)_ g(2)_ g...\) means digit representation of the real M(g) to base g. It is known that M(g) is transcendental. The author gives estimates for Mahler's function \(w_ d\)
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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.
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Acta Mathematica, 2004 This interesting article is nicely described by (selected) parts of the introduction: ``About fifty years ago \textit{K. Mahler} [Mathematika 4, 122--124 (1957; Zbl 0208.31002)] proved that if \(\alpha> 1\) is rational but not an integer and if \(01\) be a real algebraic number and let ...
CORVAJA, Pietro, ZANNIER U.
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Approximation of complex algebraic numbers by algebraic numbers of bounded degree
, 2007 We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1.
Bugeaud, Yann, Evertse, Jan-Hendrik
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On the rational approximations to the powers of an algebraic number
, 2004 12 pages, plain ...
Corvaja, Pietro, Zannier, Umberto
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Rational approximations to
Journal de théorie des nombres de Bordeaux, 2008 In this paper, we establish improved effective irrationality measures for certain numbers of the form n 3, using approximations obtained from hypergeometric functions. These results are very close to the best possible using this method. We are able to obtain these results by determining very precise arithmetic information about the denominators of the ...
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