English

An improved sum-product bound for quaternions

Combinatorics 2021-11-11 v2

Abstract

We show that there exists an absolute constant c>0c > 0, such that, for any finite set AA of quaternions, max{A+A,AA}A4/3+c. \max\{|A+A, |AA| \} \gtrsim |A|^{4/3 + c}. This generalizes a sum-product bound for real numbers proved by Konyagin and Shkredov.

Keywords

Cite

@article{arxiv.1809.02214,
  title  = {An improved sum-product bound for quaternions},
  author = {Abdul Basit and Ben Lund},
  journal= {arXiv preprint arXiv:1809.02214},
  year   = {2021}
}

Comments

Appeared in SIAM J. Discrete Math. This version corrects some errors from the previous version, and clarifies the analysis

R2 v1 2026-06-23T03:57:19.735Z