An improved sum-product bound for quaternions

Abdul Basit, Ben Lund

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


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

Original languageEnglish
Pages (from-to)1044-1060
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Issue number2
Publication statusPublished - 25 Jun 2019
Externally publishedYes


  • Additive combinatorics
  • Quaternions
  • Sum-product conjecture

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