An improved bound for the size of the set $A/A+A$

Oliver Roche-Newton

An improved bound for the size of the set $A/A+A$

Combinatorics 2018-10-26 v1

Authors: Oliver Roche-Newton

Abstract

It is established that for any finite set of positive real numbers $A$ , we have $|A/A+A| \gg \frac{|A|^{\frac{3}{2}+\frac{1}{26}}}{\log^{1/2}|A|}.$

Keywords

additive combinatorics sum-product estimates finite sets growth bounds ratio set

Cite

@article{arxiv.1810.10846,
  title  = {An improved bound for the size of the set $A/A+A$},
  author = {Oliver Roche-Newton},
  journal= {arXiv preprint arXiv:1810.10846},
  year   = {2018}
}

Comments

This paper was completed over a year ago but not submitted to arxiv at the time. A published version can be found in the Proceedings of SoCG 2018. arXiv admin note: substantial text overlap with arXiv:1801.10431

An improved bound for the size of the set $A/A+A$

Abstract

Keywords

Cite

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