Results 11 to 20 of about 3,575 (254)
A $p$-adic lower bound for a linear form in logarithms
International Journal of Number Theory, 2022 Linear forms in logarithms have an important role in the theory of Diophantine equations. In this article, we prove explicit $p$-adic lower bounds for linear forms in $p$-adic logarithms of rational numbers using Pad\'e approximations of the second kind ...
Seppälä, Louna +3 more
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Linear forms in logarithms and exponential Diophantine equations [PDF]
Hardy-Ramanujan Journal, 2020 This paper aims to show two things. Firstly the importance of Alan Baker's work on linear forms in logarithms for the development of the theory of exponential Diophantine equations.
Rob Tijdeman, Tijdeman, Rob
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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 +2 more sources
, 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 ...
Sanda Bujačić, Alan Filipin
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Journal of New TheoryThis study proves that the Diophantine equation $\left(9d^2+1\right)^x+\left(16d^2-1\right)^y=(5d)^z$ has a unique positive integer solution $(x,y,z)=(1,1,2)$, for all $d>1$.
Murat Alan, Tuba Çokoksen
doaj +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.
Maurice Mignotte +2 more
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Linear Forms in Logarithms and Applications
, 2018 International ...
Yann Bugeaud, Bugeaud, Yann
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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 ...
Yuri Nesterenko
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Hypergeometric transformations of linear forms in one logarithm
Functiones et Approximatio Commentarii Mathematici, 2008 Using both hypergeometric series and integrals, we discuss several constructions of diophantine approximations to logarithms of rational or algebraic ...
Viola, C. +4 more
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