Abstract. We give a generalization of the geometric estimate used by Hart and the second author in their 2008 work on sums and products in finite fields. Their result concerned level sets of non-degenerate bilinear forms over finite fields, while in this work we prove that if E ⊂ Fq is sufficiently large and ̟ is a non-degenerate multi-linear form then ̟ will attain all possible nonzero values as its arguments vary over E, under a certain quantitative assumption on the extent to which E is… Expand

We improve previous sum–product estimates in ℝ; namely, we prove the inequality max{|A + A|, |AA|} ≫ |A|4/3+c, where c is any number less than 5/9813. New lower bounds for sums of sets with small… Expand