Shatrovskii's construction of thin bases

Details Shatrovskii's construction of thin bases Shatrovskii's construction of thin bases

2009-06-06

arxiv.org/abs/0906.1241v1

Mathematics

Number Theory

8 pages

Scientific paper

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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