Sur l'inégalité de Turán–Kubilius friable

Abstract : We obtain a new form, uniform with respect to all parameters, of the friable (i.e. relevant to integers free of large prime factors) Turán-Kubilius inequality, comparing the empirical variance of an additive arithmetical function with friable support to that of its probabilistic model. Several applications are developed, significantly improving on previously known results for small values of the friability parameter. Keywords: Friable integers, additive functions, Kubilius model, Turán-Kubilius inequality.
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Régis de La Bretèche, Gérald Tenenbaum. Sur l'inégalité de Turán–Kubilius friable. Journal of the London Mathematical Society, London Mathematical Society, 2016, 93 (1), pp.175-193. ⟨10.1112/jlms/jdv051⟩. ⟨hal-01281714⟩

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