Geodesic
Effective Erd\H os--Wintner Theorems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 275-289

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The classical theorem of Erdős and Wintner furnishes a criterion for the existence of a limiting distribution for a real additive arithmetical function. This work is devoted to providing an effective estimate for the remainder term under the assumption that the conditions in the criterion are fulfilled. We also investigate the case of a conditional distribution.
Keywords: distribution of real additive functions, mean values of complex multiplicative function, Erdős–Wintner theorem, effective averages, number of prime factors. 
@article{TM_2021_314_a11,
     author = {G\'erald Tenenbaum and Johann Verwee},
     title = {Effective {Erd\H} {os--Wintner} {Theorems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {275--289},
     publisher = {mathdoc},
     volume = {314},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_314_a11/}
}
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Gérald Tenenbaum; Johann Verwee. Effective Erd\H os--Wintner Theorems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 275-289. http://geodesic.mathdoc.fr/item/TM_2021_314_a11/