Minorations simultanées de formes linéaires de logarithmes de nombres algébriques

Details Minorations simultanées de formes linéaires de logarithmes de nombres algébriques Minorations simultanées de formes linéaires de logarithmes de nombres algébriques

2010-04-21

arxiv.org/abs/1004.3652v2

Mathematics

Number Theory

30p

Scientific paper

This work falls within the theory of linear forms in logarithms over a commutative linear group defined over a number field. We give lower bounds for simultaneous linear forms in logarithms of algebraic numbers, treating both the archimedean and $p$-adic cases. The proof includes Baker's method, Hirata's reduction, Chudnovsky's process of variable change. The novelty is that we integrated into the proof the modern tools of adelic slope theory, using also a new small values Siegel's lemma.

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