Sum-product phenomenon in finite fields not of prime order
Journal
Rocky Mountain Journal of Mathematics
Journal Volume
41
Journal Issue
3
Pages
941-948
Date Issued
2011
Author(s)
Abstract
Let F = Fpn be a finite field and A a subset of F so that for any A′ C A with |A′| ≥|A|15/16 and for any G C F a subfield (not necessarily proper) and for any elements c, d ∈ F if A′ C cG + d, then |A′| ≤|G|1/2. Then it must be that max(|A + A|,|F(A,A)|)>≈|A|17/16where F : Fp× Fp → Fp is a function defined by F(x, y) = x(g(x) + cy), where c ∈ Fp* and g : Fp → F p is any function. The case g = 0 and c = 1 improves the exponent in [6] from 20/19 to 17/16. © 2011 Rocky Mountain Mathematics Consortium.
Type
journal article