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Combinatorial Nullstellensatz approach to polynomial expansion

Volume 165 / 2014

Fedor Petrov Acta Arithmetica 165 (2014), 279-282 MSC: Primary 12E05; Secondary 05E40. DOI: 10.4064/aa165-3-6

Abstract

Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of $|f(A,B)|$ for finite subsets $A$, $B$ of a field, and a polynomial $f(x,y)$ of the form $f(x,y)=g(x)+yh(x)$, where the degree of $g$ is greater than that of $h$.

Authors

  • Fedor PetrovSt. Petersburg Department
    of V. A. Steklov Institute of Mathematics RAS
    Fontanka 27
    191023 St. Petersburg, Russia
    and
    Faculty of Mathematics and Mechanics
    St. Petersburg State University
    Universitetsky prospekt, 28
    198504 Peterhof, St. Petersburg, Russia
    e-mail

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