Settling the Optimal Exponent Relating Sumsets and Difference Sets

Haowei Lin, Shanda Li

For a finite nonempty subset $A$ of an abelian group, let $\sigma (A)=|A+A|/|A|$ and $\delta (A)=|A-A|/|A|$. The classical sum-difference inequalities state that $$σ(A)^{1/2}\leqδ(A)\leqσ(A)^2…