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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 276, Pages 262–265 (Mi tm3365)  
A note on the distribution of some additive functions

Gérald Tenenbaum

Institut Élie Cartan, Université Henri Poincaré — Nancy 1, Vandœuvre-lès-Nancy, France
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Abstract: Let $f$ denote an additive arithmetical function with continuous limiting distribution $F$ on the integers. Then $f$ also has a limiting distribution $G$ on shifted primes. Under some growth conditions on the values of $f$ at primes, we provide optimal lower bounds for the modulus of continuity of $F$ and $G$, at all points from a specified infinite set.
Received in June 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 276, Pages 257–260
DOI: https://doi.org/10.1134/S0081543812010221
Bibliographic databases:
Document Type: Article
UDC: 511.335
Language: English
Citation: Gérald Tenenbaum, “A note on the distribution of some additive functions”, Number theory, algebra, and analysis, Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 276, MAIK Nauka/Interperiodica, Moscow, 2012, 262–265; Proc. Steklov Inst. Math., 276 (2012), 257–260
Citation in format AMSBIB
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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