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In this paper we consider an extension to friable integers of the arcsine law for the mean distribution of the divisors of integers, originally due to Deshouillers, Dress and Tenenbaum.We describe the limit law and show that it departs from the arcsine law when the friability parameter increases. More precisely, as , the mean distribution shifts from the arcsine law towards Gaussian behaviour.
Soit un sous-intervalle de ; on montre que la probabilité pour qu’un diviseur d’un entier appartiennent à possède une loi de distribution dont la mesure de répartition est atomique, à support inclus dans l’ensemble des nombres dyadiques.
A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.
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