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Sur l'inégalité de Turán–Kubilius friable
Author(s) -
de la Bretèche Régis,
Tenenbaum Gérald
Publication year - 2016
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdv051
Subject(s) - mathematics , friability , humanities , prime (order theory) , arithmetic function , statistics , combinatorics , discrete mathematics , philosophy , physics , nuclear magnetic resonance , ethyl cellulose , polymer
We obtain a new form, uniform with respect to all parameters, of the friable (that is, 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.