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Chebyshevskii Sbornik, 2016, Volume 17, Issue 4, Pages 51–56
DOI: https://doi.org/10.22405/2226-8383-2016-17-4-51-56 (Mi cheb515) 		 
Romanoff additive theorem's proof and its analogues

A. N. Vassilyev

Kazakhstan Branch of Lomonosov Moscow State University, Astana
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DOI: https://doi.org/10.22405/2226-8383-2016-17-4-51-56
Abstract: In paper we describe the way N. P. Romanoff proved his additive theorem and sufficient conditions to obtain its analogues for sets with similar distribution and arithmetic. Also the example of set with similar distribution but with different arithmetic is given. We prove that the Romanoff theorem's analogue for this set is incorrect.
Bibliography: 9 titles.
Keywords: Romanoff theorem, sumset, exponential sums.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan ГФ4-0816
Received: 15.05.2016
Accepted: 12.12.2016
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: A. N. Vassilyev, “Romanoff additive theorem's proof and its analogues”, Chebyshevskii Sb., 17:4 (2016), 51–56
Citation in format AMSBIB
\Bibitem{Vas16}
\by A.~N.~Vassilyev
\paper Romanoff additive theorem's proof and its analogues
\jour Chebyshevskii Sb.
\yr 2016
\vol 17
\issue 4
\pages 51--56
\mathnet{http://mi.mathnet.ru/cheb515}
\crossref{https://doi.org/10.22405/2226-8383-2016-17-4-51-56}
\elib{https://elibrary.ru/item.asp?id=27708204}
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