Results 241 to 250 of about 7,373 (275)

Linear forms in elliptic logarithms

Journal für die reine und angewandte Mathematik (Crelles Journal), 2009
One of the main challenges in the theory of linear forms in elliptic logarithms was raised by S.~Lang in 1964 [\textit{S. Lang}, ''Diophantine approximations on toruses.'' Am. J. Math. 86, 521--533 (1964; Zbl 0142.29601)]. The goal was to produce a lower bound for a linear combination of logarithms of algebraic points on an elliptic curve, with an ...
David, Sinnou, Hirata-Kohno, Noriko
openaire   +1 more source

IMPROVED ESTIMATE FOR A LINEAR FORM OF THE LOGARITHMS OF ALGEBRAIC NUMBERS

Sbornik: Mathematics, 1968
L P Sil'Nikov, V P Palamodov, Ju L Smul'Jan   +2 more
exaly   +2 more sources

Linear Forms in Logarithms

2016
Hilbert's problems form a list of twenty-three problems in mathematics published by David Hilbert, a German mathematician, in 1900. The problems were all unsolved at the time and several of them were very influential for the 20th century mathematics. Hilbert believed it was essential for mathematicians to find new machineries and methods in order to ...
Bujačić Babić, Sanda, Filipin, Alan
openaire   +2 more sources

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
openaire   +1 more source

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.
openaire   +2 more sources

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.
openaire   +1 more source

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.
openaire   +1 more source

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 ...
openaire   +1 more source

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.
openaire   +1 more source

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.
openaire   +2 more sources