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Fourier methods and non degenerate polynomials

We use Fourier methods to give a shorter proof of Vu's result and extend it to a more general setting, namely: For any non-degenerate polynomials f(x,y)∈Fq[x,y] and A,B,C,D⊂Fq, either we have|A+C||B+D||f(A,B)|≳|A||B|q, or|A+C||B+D||f(A,B)|2≳|A|2|B|2|C||D|q.

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Bibliographic Details
Published in:Finite fields and their applications 2018-09, Vol.53, p.140-143
Main Author: Shen, Chun-Yen
Format: Article
Language:English
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Summary:We use Fourier methods to give a shorter proof of Vu's result and extend it to a more general setting, namely: For any non-degenerate polynomials f(x,y)∈Fq[x,y] and A,B,C,D⊂Fq, either we have|A+C||B+D||f(A,B)|≳|A||B|q, or|A+C||B+D||f(A,B)|2≳|A|2|B|2|C||D|q.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2018.06.002