%0 Journal Article
%T Sum-product estimates for rational functions
%A Boris Bukh
%A Jacob Tsimerman
%J Mathematics
%D 2010
%I arXiv
%R 10.1112/plms/pdr018
%X We establish several sum-product estimates over finite fields that involve polynomials and rational functions. First, |f(A)+f(A)|+|AA| is substantially larger than |A| for an arbitrary polynomial f over F_p. Second, a characterization is given for the rational functions f and g for which |f(A)+f(A)|+|g(A,A)| can be as small as |A|, for large |A|. Third, we show that under mild conditions on f, |f(A,A)| is substantially larger than |A|, provided |A| is large. We also present a conjecture on what the general sum-product result should be.
%U http://arxiv.org/abs/1002.2554v2