Results 11 to 20 of about 56,412,384 (265)
On the approximation to algebraic numbers by algebraic numbers [PDF]
Glasnik matematički, 2009 Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number ε, there are infinitely many algebraic numbers α of degree at most n such that |ξ - α| < H(α)-n - 1 + ε, where H(α) denotes the naive height of α.
Yann Bugeaud, Bugeaud, Yann
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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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On simultaneous approximation of algebraic numbers [PDF]
Mathematika, 2022 Let $Γ\subset \bar{\mathbb Q}^{\times}$ be a finitely generated multiplicative group of algebraic numbers. Let $α_1,\ldots,α_r\in\bar{\mathbb Q}^\times$ be algebraic numbers which are $\mathbb{Q}$-linearly independent and let $ε>0$ be a given real number.
Kumar, Veekesh, Thangadurai, R.
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Heights and multiplicative relations on algebraic varieties [PDF]
, 2007 Points on a subvariety X of a semi-abelian variety A that are contained in a subgroup, let the subgroup be of finite rank or algebraic, are subject to severe restrictions arithmetical nature. Finiteness results for intersections of X with subgroups of
Habegger, Philipp
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Approximation of p-adic numbers by algebraic numbers of bounded degree [PDF]
, 1978 The approximation of p-adic numbers by algebraic numbers of bounded degree is studied. Results similar to those obtained by Wirsing and by Davenport and Schmidt in the real case are proved in the p-adic case.
Morrison, John F.
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On approximation to real numbers by algebraic numbers [PDF]
Acta Arithmetica, 2000 Define the height \(H(\alpha)\) of an algebraic number \(\alpha\) as the maximum of the absolute values of the coefficients of its irreducible polynomial over \(\mathbb{Z}\). Let \(n\geq 2\) be an integer and let \(\xi\) be a real number which is not an algebraic number of degree \(\leq n\).
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Algebraic entropy for algebraic maps [PDF]
, 2015 We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map.
Hone, A. N. W. +4 more
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Diophantine approximation by conjugate algebraic numbers
, 2006 In 1969, Davenport and Schmidt provided upper bounds for the approximation of a real number by algebraic integers. Their novel approach was based on the geometry of numbers and involved the duality for convex bodies.
Alain, Guillaume
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On approximation of real numbers by algebraic numbers of bounded degree [PDF]
, 2007 Dirichlet proved that for any real irrational number ξ there exist infinitely many rational numbers p/q such that |ξ−p/q|2, is still unknown.
Kiryl I. Tsishchanka +1 more
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Approximation to certain transcendental decimal fractions by algebraic numbers [PDF]
, 1991 In this paper, we treat certain decimal fractions defined by Mahler and study approximations to these numbers by algebraic numbers of bounded degree. For this purpose, we give an estimate for the values of Mahler's function wd and of Koksma's function wd*
Amou, Masaaki
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