Abstract:
An analog of the Turan'n–Kubilyus inequality is proved for a sufficiently wide class of sequences which contains, in particular, an=f(n) and an=f(pn), where f(n) is a polynomial with integral coefficients. This result helps us to obtain integral limit theorems for additive functions on the class of sequences under investigation.
Citation:
B. V. Levin, N. M. Timofeev, “The analogue of the law of large numbers for additive functions on sparse sets”, Mat. Zametki, 18:5 (1975), 687–698; Math. Notes, 18:5 (1975), 1000–1006
\Bibitem{LevTim75}
\by B.~V.~Levin, N.~M.~Timofeev
\paper The analogue of the law of large numbers for additive functions on sparse sets
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 5
\pages 687--698
\mathnet{http://mi.mathnet.ru/mzm7680}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=399028}
\zmath{https://zbmath.org/?q=an:0318.10040}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 5
\pages 1000--1006
\crossref{https://doi.org/10.1007/BF01153566}
Linking options:
https://www.mathnet.ru/eng/mzm7680
https://www.mathnet.ru/eng/mzm/v18/i5/p687
This publication is cited in the following 1 articles:
G. I. Arkhipov, V. G. Zhuravlev, V. A. Iskovskikh, A. A. Karatsuba, M. B. Levina-Khripunova, V. N. Chubarikov, A. A. Yudin, “Nikolai Mikhailovich Timofeev (obituary)”, Russian Math. Surveys, 58:4 (2003), 773–776
Citation in format AMSBIB
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