Results 241 to 250 of about 7,365 (273)

Applications of Linear Forms in Logarithms

2008
A linear form in logarithms of algebraic numbers is an expression of the form $$ \beta _1 \log \alpha _1 + \cdots + \beta _n log \alpha _n , $$ where the α’s and the β’s denote complex algebraic numbers, and log denotes any determination of the logarithm.
Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte   +2 more
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Linear forms in the logarithms of algebraic numbers

Mathematika, 1966
In 1934 Gelfond [2] and Schneider [6] proved, independently, that the logarithm of an algebraic number to an algebraic base, other than 0 or 1, is either rational or transcendental and thereby solved the famous seventh problem of Hilbert. Among the many subsequent developments (cf.
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On Baker's inequality for linear forms in logarithms

Mathematical Proceedings of the Cambridge Philosophical Society, 1976
AbstractLet 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 the logarithms of algebraic numbers

1993
This 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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Linear Forms in Logarithms

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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Linear Forms in Logarithms of Rational Numbers

2008
The 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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Linear forms in \(p\)-adic logarithms. III

1990
Ce 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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Asymptotic formulae for linear functional forms in two logarithms

Russian Mathematical Surveys, 1983
Translation from Usp. Mat. Nauk 38, No.1(229), 193-194 (Russian) (1983; Zbl 0533.30035).
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Linear forms in logarithms

2022
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Linear Rescaling to Accurately Interpret Logarithms

Journal of Econometric Methods, 2023
Nick Huntington-Klein
exaly