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arXiv · 0906.1241

Shatrovskii's construction of thin bases

Melvyn B. Nathanson
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Abstract

The set A of nonnegative integers is called a basis of order h if every nonnegative integer can be represented as the sum of exactly h not necessarily distinct elements of A. An additive basis A of order h is called thin if there exists c > 0 such that the number of elements of A not exceeding x is less than cx^{1/h} for all x > 0. This paper describes a construction of Shatrovskii of thin bases of order h.

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Melvyn B. Nathanson. 2009-06-06. Shatrovskii's construction of thin bases. https://arxiv.org/abs/0906.1241

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