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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 2, Pages 179–204 (Mi izv18)  

This article is cited in 2 scientific papers (total in 3 papers)

Integral limit theorems for sums of additive functions with shifted arguments

N. M. Timofeev

Vladimir State Pedagogical University

Abstract: In this paper we find necessary and sufficient conditions for the vanishing of the limit distribution for a linear combination of two real-valued additive functions. We obtain results for $g_1(an+b)/B_1(x)+g_2(cn+d)/B_2(x)-A(x)$, where $a>0$, $b,c>0$, and $d$ are integers with $ad-bc\ne 0$, that are almost as strong as in the case of a single additive function. As an application, we resolve a conjecture of Katai.

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English version:
Izvestiya: Mathematics, 1995, 59:2, 401–426

Bibliographic databases:

MSC: 11K36
Received: 20.02.1994

Citation: N. M. Timofeev, “Integral limit theorems for sums of additive functions with shifted arguments”, Izv. RAN. Ser. Mat., 59:2 (1995), 179–204; Izv. Math., 59:2 (1995), 401–426

Citation in format AMSBIB
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\by N.~M.~Timofeev
\paper Integral limit theorems for sums of additive functions with shifted arguments
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 2
\pages 179--204
\mathnet{http://mi.mathnet.ru/izv18}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1337165}
\zmath{https://zbmath.org/?q=an:0894.11034}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 2
\pages 401--426
\crossref{https://doi.org/10.1070/IM1995v059n02ABEH000018}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ88800009}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mauclaire J., “A Characterization of Some Additive Arithmetical Functions, III”, Acta Arith., 91:3 (1999), 229–232  mathscinet  zmath  isi
    2. Mauclaire J.-L., “Some Results on Additive Arithmetical Functions with Values in a Group”, Analytic and Probabilistic Methods in Number Theory, eds. Dubickas A., Laurincikas A., Manstavicius E., Tev Ltd, 2002, 200–220  mathscinet  zmath  isi
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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