Results 231 to 240 of about 3,579 (260)

Linear forms in the logarithms of algebraic numbers

Lecture Notes in Mathematics, 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.
Vladimir G Sprindzuk
exaly   +2 more sources

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.
exaly   +3 more sources

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.
O Yu Aristov, I V Astashova, A V Malyutin   +2 more
exaly   +2 more sources

Linear Forms in Logarithms of Rational Numbers [PDF]

, 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 ...
Yuri Nesterenko
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Linear forms in logarithms [PDF]

, 1975
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Linear forms in the logarithms of algebraic numbers (II)

Mathematika, 1967
exaly   +3 more sources

A new approach to Baker's theorem on linear forms in logarithms I

Lecture Notes in Mathematics, 1987
G Wüstholz
exaly   +2 more sources

Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms [PDF]

Acta Arithmetica, 1994
In order to compute all integer points on a Weierstraß equation for an elliptic curve E/Q, one may translate the linear relation between rational points on E into a linear form of elliptic logarithms.
N Tzanakis
exaly   +3 more sources

Estimates of linear forms in logarithms [PDF]

, 1986
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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
openaire   +1 more source