Algebraic methods in sum-product phenomena

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 theorem and a theorem by Y. Stein play an important role in our proof....

Full description

Saved in:
Bibliographic Details
Published in:Israel journal of mathematics 2012-03, Vol.188 (1), p.123-130
Main Author: Shen, Chun-Yen
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 theorem and a theorem by Y. Stein play an important role in our proof.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-011-0096-3