Does anyone know a good book for learning about linear forms in logarithms especially one that is motivated by solving Diophantine equations with it? I know there's a chapter in Langs book but it doesn't have any applications so that's not the sort of thing I was looking for. Thanks very much for any recommendations!
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A couple of possibilities: Nigel P Smart, The Algorithmic Resolution of Diophantine Equations, London Mathematical Society Student Texts 41, Cambridge University Press, and Benne de Weger, Algorithms For Diophantine Equations, Centrum voor Wiskunde en Informatica, Amsterdam.
Yo should take a look at Alan Baker's Transcendental Number Theory. In chapters two and three he develops the theory of linear forms in logarithms and then he applies it to the study of some Diophantine equations.