Algebraic methods in sum-product phenomena

Details Algebraic methods in sum-product phenomena Algebraic methods in sum-product phenomena

2009-11-13

arxiv.org/abs/0911.2627v3

Mathematics

Classical Analysis and ODEs

introduction revised

Scientific paper

We classify the polynomials $f(x,y) \in \mathbb R[x,y]$ such that given any
finite set $A \subset \mathbb R$ 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.

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