Romanoff additive theorem's proof and its analogues

A. N. Vassilyev

Kazakhstan Branch of Lomonosov Moscow State University, Astana

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.

UDC: 511

Received: 15.05.2016
Accepted: 12.12.2016

DOI: 10.22405/2226-8383-2016-17-4-51-56

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