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On Baker's inequality for linear forms in logarithms
Mathematical Proceedings of the Cambridge Philosophical Society, 1976AbstractLet α1, …, αn an be non-zero algebraic numbers with degrees at most d and heights respectively Al, …, An (all Aj ≥ 4) and let b1, …, bn be rational integers with absolute values at most B (≥ 4). Denote by p a prime ideal of the field and suppose that p divides the rational prime p.
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Linear Forms in Logarithms of Rational Numbers
2008The history of the theory of linear forms in logarithms is well known. We shall briefly sketch only some of the moments connected with new technical progress and important for our article. This theory was originated by pioneer works of A.O. Gelfond (see, for example, [5, 6]); with the help of the ideas which arose in connection with the solution of 7 ...
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Asymptotic formulae for linear functional forms in two logarithms
Russian Mathematical Surveys, 1983Translation from Usp. Mat. Nauk 38, No.1(229), 193-194 (Russian) (1983; Zbl 0533.30035).
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2014
I am dealing with basic definitions of crucial mathematical concepts in linear forms in logarithms and I introduce most important theorems and proofs during five lectures. Also, I introduce some Baker type inequalities available today which are easy to apply. In order to illustrate this very important machinery I introduce some examples.
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I am dealing with basic definitions of crucial mathematical concepts in linear forms in logarithms and I introduce most important theorems and proofs during five lectures. Also, I introduce some Baker type inequalities available today which are easy to apply. In order to illustrate this very important machinery I introduce some examples.
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Linear forms in \(p\)-adic logarithms. III
1990Ce texte établit des améliorations des minorations de formes linéaires, à coefficients rationnels, de logarithmes \(p\)-adiques de nombres algébriques, obtenues dans les articles précédents de la série [I, Acta. Arith. 53, 107-186 (1989; Zbl 0699.10050) and II, Compos. Math. 74, 15-113 (1990; Zbl 0723.11034)]. L'A.
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Linear forms in the logarithms of algebraic numbers
1993This chapter is of an auxiliary nature, being mainly concerned with the relationship between bounds for linear forms in the logarithms of algebraic numbers in different (archimedean and non-archimedean) metrics. This material will later be used in the analysis of Thue and Thue-Mahler equations.
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An inequality for a linear form in the logarithms of algebraic numbers
Mathematical Notes of the Academy of Sciences of the USSR, 1969Let ln α1, ..., ln αm−1 be the logarithms of fixed algebraic numbers which are linearly independent over the field of rational numbers, b1, ..., bm−1 rational integers, δ > 0. A bound from below is deduced for the height of the algebraic number αm under the condition that ¦b1 ln α1+...+bm−1ln αm− ¦ < exp {−δH},H=max ¦ b k
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Lower bounds for linear forms in logarithms
1988P. Philippon, M. Waldschmidt
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