English

A new upper bound for finite additive bases

Number Theory 2007-05-23 v1 Combinatorics

Abstract

Let n(2,k) denote the largest integer n for which there exists a set A of k nonnegative integers such that the sumset 2A contains {0,1,2,...,n-1}. A classical problem in additive number theory is to find an upper bound for n(2,k). In this paper it is proved that limsup_{k\to\infty} n(2,k)/k^2 \leq 0.4789.

Keywords

Cite

@article{arxiv.math/0503241,
  title  = {A new upper bound for finite additive bases},
  author = {Sinan Gunturk and Melvyn B. Nathanson},
  journal= {arXiv preprint arXiv:math/0503241},
  year   = {2007}
}

Comments

19 pages; LaTex