# GÉNÉRALISATIONS QUANTITATIVES DU CRITÈRE D'INDÉPENDANCE LINÉAIRE DE NESTERENKO

Abstract : In this paper we extend Fischler's quantitative generalization of Nesterenko's linear independence criterion, by weakening the hypotheses on the divisors of the coe cients of the linear forms and allowing (to some extent) the linear forms not to tend to 0. Another version of this result is proved, in the spirit of Siegel's criterion, with a recurrence relation veri ed by the linear forms. Finally, the results are restated in a more general setting in terms of convex bodies and lattices of $\mathbb{R}^n$.
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Reports

Cited literature [18 references]

https://hal.archives-ouvertes.fr/hal-00959764
Contributor : Simon Dauguet <>
Submitted on : Monday, March 17, 2014 - 5:21:19 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
Document(s) archivé(s) le : Tuesday, June 17, 2014 - 10:56:36 AM

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• HAL Id : hal-00959764, version 1
• ARXIV : 1403.4205

### Citation

Simon Dauguet. GÉNÉRALISATIONS QUANTITATIVES DU CRITÈRE D'INDÉPENDANCE LINÉAIRE DE NESTERENKO. 2014. ⟨hal-00959764⟩

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