2009/11/13 by Chun‐Yen Shen, Shen, Chun-Yen
Computer Science · Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Limits and Structures in Graph Theory #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0911.2627
openalex publication_date 2009/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify the polynomials f(x,y) ∈ \mathbb R[x,y] such that given any finite set A ⊂ \mathbb R if |A+A| is small, then |f(A,A)| is large. In particular, the following bound holds : |A+A||f(A,A)| \gtrsim |A|5/2. The Bezout's theorem and a theorem by Y. Stein play important roles in our proof.