Year: 2011
Type: article
Abstract: 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 𝔽p. 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.
DOI: 10.1112/plms/pdr018
Authors: Boris Bukh, Jacob Tsimerman
Institutions: University of Cambridge, Princeton University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2163055716