An improved sum-product bound for quaternions

Abstract

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

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

References in corpus (3)

• On higher energy decompositions and the sum-product phenomenon
• On a theorem of Schoen and Shkredov on sumsets of convex sets
• An application of kissing numbers in sum-product estimates

Cited by in corpus (1)

• Sum-product estimates for diagonal matrices