## A quantified version of Bourgain's sum-product estimate in $\Bbb F_{p}$ for subsets of incomparable sizes

### Summary

Summary: Let Fp be the field of residue classes modulo a prime number p. In this paper we prove that if A, B $\subset F\ast$p, then for any fixed $\epsilon > 0$, p $1/25 - \epsilon$|A + A| + |AB| min |B|, |A|.

11B75, 11T23