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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 314, Pages 275–289
DOI: https://doi.org/10.4213/tm4162 (Mi tm4162) 		 
Effective Erdős–Wintner Theorems

Gérald Tenenbaum, Johann Verwee

Institut Élie Cartan, Université de Lorraine, BP 70239, 54506 Vandœuvre-lès-Nancy Cedex, France
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DOI: https://doi.org/10.4213/tm4162
Abstract: 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.
Received: February 18, 2020
Revised: February 28, 2021
Accepted: May 2, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 314, Pages 264–278
DOI: https://doi.org/10.1134/S008154382104012X
Bibliographic databases:
Document Type: Article
UDC: 511.75+519.213
MSC: 11N25, 11N37, 11N60
Language: Russian
Citation: Gérald Tenenbaum, Johann Verwee, “Effective Erdős–Wintner Theorems”, Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 314, Steklov Math. Inst., Moscow, 2021, 275–289; Proc. Steklov Inst. Math., 314 (2021), 264–278
Citation in format AMSBIB
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\paper Effective Erd\H os--Wintner Theorems
\inbook Analytic and Combinatorial Number Theory
\bookinfo Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 314
\pages 275--289
\publ Steklov Math. Inst.
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4162}
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\jour Proc. Steklov Inst. Math.
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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