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Minorations explicites de formes linéaires en deux logarithmes

Abstract : The lower bounds for linear combinations with integer coefficients of algebraic number of logarithms are important tools in towards the effective resolution of some diophantine equation classes. On this context the particular case of two logarithms is especially useful. To obtain such lower bounds we use here the so-called Schneider's method with multiplicity. The proof is based on the use of interpolation determinants and on a multiplicity estimate. Our multiplicity estimate, whose proof is reminiscent of the original method due to D.W. Masser, appears, in our case, to be more efficient than the general statements previously employed. We use a standard method to obtain a lower and an upper bound for some non zero determinant that enables us to obtain a fondamental inequality containing many arbitrary parameters. We can deduce from this last inequality a list of lower bounds which are totally explicit for linear forms of logarithms.
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Contributor : Nicolas Gouillon <>
Submitted on : Thursday, December 11, 2003 - 4:20:45 PM
Last modification on : Thursday, January 18, 2018 - 1:25:31 AM
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  • HAL Id : tel-00003964, version 1



Nicolas Gouillon. Minorations explicites de formes linéaires en deux logarithmes. Mathématiques [math]. Université de la Méditerranée - Aix-Marseille II, 2003. Français. ⟨tel-00003964⟩



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