Algebraic methods in sum-product phenomena
Journal
Israel Journal of Mathematics
Journal Volume
188
Journal Issue
1
Pages
123-130
Date Issued
2012
Author(s)
Abstract
We classify the polynomials f(x, y) ∈ ℝ[x, y] such that, given any finite set A ⊂ ℝ, if {Pipe}A + A{Pipe} is small, then {Pipe}f(A,A){Pipe} is large. In particular, the following bound holds: {Pipe}A + A{norm of matrix}f(A,A){Pipe} ≳ {Pipe}A{Pipe}5/2. The Bezout theorem and a theorem by Y. Stein play an important role in our proof. © 2011 Hebrew University Magnes Press.
Type
journal article