Algebraic methods in sum-product phenomena

الأصل · EN

We classify the polynomials f(x,y) ∈ R[x,y] such that given any finite set A ⊂ R if |A+A| is small, then |f(A,A)| is large. In particular, the following bound holds: |A+A||f(A,A)| |A|⁵/². The Bezout's theorem and a theorem by Y. Stein play important roles in our proof.