Results 221 to 230 of about 92,871 (258)

The Hilbert polynomial and linear forms in the logarithms of algebraic numbers

Izvestiya: Mathematics, 2008
We prove a new estimate for homogeneous linear forms with integer coefficients in the logarithms of algebraic numbers. We obtain a qualitative improvement of the estimate depending on the coefficients of the linear form and the best value of the constant in the estimate in the case when the number of logarithms is not too large.
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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, 1969
Let 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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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
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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
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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 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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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

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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